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This article is about entropy in thermodynamics. For entropy in information theory, see Information entropy. For other uses, see Entropy (disambiguation).
For a generally accessible and less technical introduction to the topic, see Introduction to entropy. Thermodynamic Entropy provides a measure of certain aspects of Energy in relation to Absolute temperature.
Ice melting - a classic example of entropy increasing described in 1862 by Rudolf Clausius as an increase in the disgregation of the molecules of the body of ice.
Ice melting - a classic example of entropy increasing[1] described in 1862 by Rudolf Clausius as an increase in the disgregation of the molecules of the body of ice. In Thermodynamics (a branch of Physics) entropy, symbolized by S, is a measure of the unavailability of a system ’s Energy Rudolf Julius Emanuel Clausius (Born Rudolf Gottlieb, January 2, 1822 &ndash August 24, 1888) was a German Physicist In the History of thermodynamics, disgregation was defined in 1862 by Rudolf Clausius as the magnitude of the degree in which the molecules of a body are separated [2]
Entropy articles
Introduction
History
Classical
Statistical

In thermodynamics (a branch of physics), entropy is a measure of the unavailability of a system’s energy to do work. Thermodynamic Entropy provides a measure of certain aspects of Energy in relation to Absolute temperature. The concept of Entropy developed in response to the observation that a certain amount of functional energy released from Combustion reactions is always lost to dissipation In Thermodynamics, entropy is a measure of how close a Thermodynamic system is to equilibrium In Thermodynamics, statistical entropy is the modeling of the energetic function Entropy using Probability theory. In Physics, thermodynamics (from the Greek θερμη therme meaning " Heat " and δυναμις dynamis meaning " Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. In Thermodynamics, a thermodynamic system, originally called a working substance, is defined as that part of the universe that is under consideration In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός In Thermodynamics, work is the quantity of Energy transferred from one system to another without an accompanying transfer of Entropy. [3][4]

It is a measure of the randomness of molecules in a system and is central to the second law of thermodynamics and the fundamental thermodynamic relation, which deal with physical processes and whether they occur spontaneously. The second law of Thermodynamics is an expression of the universal law of increasing Entropy, stating that the entropy of an Isolated system which In Thermodynamics, the fundamental thermodynamic relation is a mathematical summation of the First law of thermodynamics and the Second law of thermodynamics Spontaneous changes, in isolated systems, occur with an increase in entropy. A spontaneous process is the time-evolution of a system in which it releases free energy (most often as heat and moves to a lower more thermodynamically stable energy state In the Natural sciences an isolated system, as contrasted with a open system, is a Physical system that does not interact with its Surroundings Spontaneous changes tend to smooth out differences in temperature, pressure, density, and chemical potential that may exist in a system, and entropy is thus a measure of how far this smoothing-out process has progressed. Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface The density of a material is defined as its Mass per unit Volume: \rho = \frac{m}{V} Different materials usually have different In Thermodynamics and Chemistry, chemical potential, symbolized by μ, is a term introduced by the American engineer chemist and mathematical

The word "entropy" is derived from the Greek εντροπία "a turning toward" (εν- "in" + τροπή "a turning"), and is symbolized by S in physics. Greek (el ελληνική γλώσσα or simply el ελληνικά — "Hellenic" is an Indo-European language, spoken today by 15-22 million people mainly

Contents

Abstract

When a system's energy is defined as the sum of its "useful" energy, (e. g. that used to push a piston), and its "useless energy", i. e. that energy which cannot be used for external work, then entropy may be (most concretely) visualized as the "scrap" or "useless" energy whose energetic prevalence over the total energy of a system is directly proportional to the absolute temperature of the considered system. In Thermodynamics, work is the quantity of Energy transferred from one system to another without an accompanying transfer of Entropy. In Thermodynamics, a thermodynamic system, originally called a working substance, is defined as that part of the universe that is under consideration (Note the product "TS" in the Gibbs free energy or Helmholtz free energy relations). In Thermodynamics, the Gibbs free energy ( IUPAC recommended name Gibbs energy or Gibbs function) is a Thermodynamic potential which In Thermodynamics, the Helmholtz free energy is a Thermodynamic potential which measures the “useful” work obtainable from a closed thermodynamic

Entropy is a function of a quantity of heat which shows the possibility of conversion of that heat into work. The increase in entropy is small when heat is added at high temperature and is greater when heat is added at lower temperature. Thus for maximum entropy there is minimum availability for conversion into work and for minimum entropy there is maximum availability for conversion into work.

Entropy S \, is not defined directly, but rather by an equation relating the change in entropy of the system to the change in heat of the system. For a constant temperature, the change in entropy \Delta S \, is defined by the equation \Delta S = \Delta Q / T \,, where \Delta Q \, is the amount of heat absorbed in an isothermal and reversible process in which the system goes from one state to another, and T \, is the absolute temperature at which the process is occurring. In Physics, heat, symbolized by Q, is Energy transferred from one body or system to another due to a difference in Temperature For articles on other forms of reversibility including reversibility of microscopic dynamics see Reversibility (disambiguation. A thermodynamic state is the macroscopic condition of a Thermodynamic system as described by its particular thermodynamic parameters. Thermodynamic temperature is the absolute measure of Temperature and is one of the principal parameters of Thermodynamics. [5] If the temperature of the system is not constant, then the relationship becomes a differential equation dS = dQ / T \, . To understand what this equation means, suppose the temperature T \, can be expressed as a function T(Q) \, of the heat Q \, . Then the total change in entropy as the heat-level varies is \Delta S = \int_A \frac{ 1 }{ T(Q)} dQ \,\!, where A \, is the set defining the range of heat values in the system.

Entropy is one of the factors that determines the free energy of the system. In Thermodynamics, the term thermodynamic free energy refers to the amount of work that can be extracted from a System, and is helpful in Engineering This thermodynamic definition of entropy is only valid for a system in equilibrium (because temperature is defined only for a system in equilibrium), while the statistical definition of entropy (see below) applies to any system. Thus the statistical definition is usually considered the fundamental definition of entropy.

Entropy increase has often been defined as a change to a more disordered state at a molecular level. In thermodynamics Entropy is often associated with the amount of Order, disorder and/or Chaos in a Thermodynamic system. In recent years, entropy has been interpreted in terms of the "dispersal" of energy. The thermodynamic concept of entropy can be described qualitatively as a measure of energy dispersal (energy distribution at a specific temperature Entropy is an extensive state function that accounts for the effects of irreversibility in thermodynamic systems. In the Physical sciences an intensive property (also called a bulk property) is a Physical property of a system that does not depend on the In Thermodynamics, a state function, state quantity, or a function of state, is a property of a system that depends only on the current In science a Process that is not reversible is called irreversible. In Thermodynamics, a thermodynamic system, originally called a working substance, is defined as that part of the universe that is under consideration

In terms of statistical mechanics, the entropy describes the number of the possible microscopic configurations of the system. Statistical mechanics is the application of Probability theory, which includes mathematical tools for dealing with large populations to the field of Mechanics In Statistical mechanics, a microstate describes a specific detailed microscopic configuration of a system that the system visits in the course of its thermal fluctuations The statistical definition of entropy is the more fundamental definition, from which all other definitions and all properties of entropy follow.

Origin of concept

The first law of thermodynamics, formalized through the heat-friction experiments of James Joule in 1843, deals with the concept of energy, which is conserved in all processes; the first law, however, lacks in its ability to quantify the effects of friction and dissipation. In Thermodynamics, the first law of thermodynamics is an expression of the more universal physical law of the Conservation of energy. James Prescott Joule FRS (ˈdʒuːl December 24, 1818 &ndash October 11, 1889) was an English Physicist In Physics, the law of conservation of energy states that the total amount of Energy in an isolated system remains constant and cannot be created although it may Friction is the Force resisting the relative motion of two Surfaces in contact or a surface in contact with a fluid (e In Physics, dissipation embodies the concept of a Dynamical system where important mechanical modes such as Waves or Oscillations lose Energy

The concept of entropy was developed in the 1850s by German physicist Rudolf Clausius who described it as the transformation-content, i. Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. Rudolf Julius Emanuel Clausius (Born Rudolf Gottlieb, January 2, 1822 &ndash August 24, 1888) was a German Physicist e. dissipative energy use, of a thermodynamic system or working body of chemical species during a change of state. In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός In Thermodynamics, a thermodynamic system, originally called a working substance, is defined as that part of the universe that is under consideration In Thermodynamics, a thermodynamic system, originally called a working substance, is defined as that part of the universe that is under consideration Chemical species are Atoms Molecules molecular fragments Ions etc A thermodynamic state is the macroscopic condition of a Thermodynamic system as described by its particular thermodynamic parameters. [6]

Although the concept of entropy was originally a thermodynamic construct, it has been adapted in other fields of study, including information theory, psychodynamics, thermoeconomics, and evolution. Information theory is a branch of Applied mathematics and Electrical engineering involving the quantification of Information. Psychodynamics, is the systematized study and theory of the psychological forces that underlie human behavior emphasizing the interplay between unconscious and conscious motivation and Thermoeconomics is the name given to a type of heterodox economic theory that attempts to explicitly apply the principles of Thermodynamics to Economics eVolution is the third Album by eLDee, it was due to be released in 2008 [7][8][9]

History

Rudolf Clausius - originator of the concept of "entropy".
Rudolf Clausius - originator of the concept of "entropy". Rudolf Julius Emanuel Clausius (Born Rudolf Gottlieb, January 2, 1822 &ndash August 24, 1888) was a German Physicist
Main article: History of entropy

The history of entropy begins with the work of French mathematician Lazare Carnot who in his 1803 paper Fundamental Principles of Equilibrium and Movement proposed that in any machine the accelerations and shocks of the moving parts all represent losses of moment of activity. The concept of Entropy developed in response to the observation that a certain amount of functional energy released from Combustion reactions is always lost to dissipation This article is about the country For a topic outline on this subject see List of basic France topics. Lazare Nicolas Marguerite Comte Carnot ( May 13, 1753 &mdash August 2, 1823) the Organizer of Victory in the French In other words, in any natural process there exists an inherent tendency towards the dissipation of useful energy. Building on this work, in 1824 Lazare's son Sadi Carnot published Reflections on the Motive Power of Fire in which he set forth the view that in all heat-engines whenever "caloric", or what is now known as heat, falls through a temperature difference, that work or motive power can be produced from the actions of the "fall of caloric" between a hot and cold body. Nicolas Léonard Sadi Carnot (1 June 1796 &ndash 24 August 1832 was a French Physicist and Military engineer who in his 1824 Reflections In Physics, heat, symbolized by Q, is Energy transferred from one body or system to another due to a difference in Temperature In Thermodynamics, motive power is an agency as Water or Steam, used to impart motion. This was an early insight into the second law of thermodynamics. The second law of Thermodynamics is an expression of the universal law of increasing Entropy, stating that the entropy of an Isolated system which

Carnot based his views of heat partially on the early 18th century "Newtonian hypothesis" that both heat and light were types of indestructible forms of matter, which are attracted and repelled by other matter, and partially on the contemporary views of Count Rumford who showed in 1789 that heat could be created by friction as when cannon bores are machined. Sir Benjamin Thompson, Count Rumford (in German: de Reichsgraf von Rumford FRS ( 26 March 1753 – 21 August 1814 [10] Accordingly, Carnot reasoned that if the body of the working substance, such as a body of steam, is brought back to its original state (temperature and pressure) at the end of a complete engine cycle, that "no change occurs in the condition of the working body. The Carnot cycle is a particular Thermodynamic cycle, modeled on the hypothetical Carnot heat engine, proposed by Nicolas Léonard Sadi Carnot in 1824 and " This latter comment was amended in his foot notes, and it was this comment that led to the development of entropy.

In the 1850s and 60s, German physicist Rudolf Clausius gravely objected to this latter supposition, i. Rudolf Julius Emanuel Clausius (Born Rudolf Gottlieb, January 2, 1822 &ndash August 24, 1888) was a German Physicist e. that no change occurs in the working body, and gave this "change" a mathematical interpretation by questioning the nature of the inherent loss of usable heat when work is done, e. g. heat produced by friction. [6] This was in contrast to earlier views, based on the theories of Isaac Newton, that heat was an indestructible particle that had mass. Sir Isaac Newton, FRS (ˈnjuːtən 4 January 1643 31 March 1727) Biography Early years See also Isaac Newton's early life and achievements Later, scientists such as Ludwig Boltzmann, Josiah Willard Gibbs, and James Clerk Maxwell gave entropy a statistical basis. Ludwig Eduard Boltzmann ( February 20, 1844 &ndash September 5, 1906) was an Austrian Physicist famous for his founding Josiah Willard Gibbs ( February 11, 1839 &ndash April 28, 1903) was an American theoretical Physicist, Chemist James Clerk Maxwell (13 June 1831 &ndash 5 November 1879 was a Scottish mathematician and theoretical physicist. Carathéodory linked entropy with a mathematical definition of irreversibility, in terms of trajectories and integrability. Constantin Carathéodory (or Constantine Karatheodoris ( Greek: Κωνσταντίνος Καραθεοδωρή ( September 13, 1873 &ndash February

Definitions and descriptions

In science, the term "entropy" is generally interpreted in three distinct, but semi-related, ways, i. e. from macroscopic viewpoint (classical thermodynamics), a microscopic viewpoint (statistical thermodynamics), and an information viewpoint (information theory). Classical thermodynamics is a branch of Physics developed in the nineteenth century by Sadi Carnot (1824 Emile Clapeyron (1834 Rudolf Clausius In Thermodynamics, statistical thermodynamics is the study of the microscopic behaviors of Thermodynamic systems using Probability theory. Information theory is a branch of Applied mathematics and Electrical engineering involving the quantification of Information.

The statistical definition of entropy (see below) is the fundamental definition because the other two can be mathematically derived from it, but not vice versa. All properties of entropy (including second law of thermodynamics) follow from this definition. The second law of Thermodynamics is an expression of the universal law of increasing Entropy, stating that the entropy of an Isolated system which

Macroscopic viewpoint (classical thermodynamics)

Conjugate variables
of thermodynamics
Pressure Volume
(Stress) (Strain)
Temperature Entropy
Chem. potential Particle no.
Main article: Entropy (classical thermodynamics)

In a thermodynamic system, a "universe" consisting of "surroundings" and "systems" and made up of quantities of matter, its pressure differences, density differences, and temperature differences all tend to equalize over time - simply because equilibrium state has higher probability (more possible combinations of microstates) than any other - see statistical mechanics. In Thermodynamics, the Internal energy of a system is expressed in terms of pairs of conjugate variables such as temperature/entropy or pressure/volume Pressure (symbol 'p' is the force per unit Area applied to an object in a direction perpendicular to the surface The volume of any solid plasma vacuum or theoretical object is how much three- Dimensional space it occupies often quantified numerically Stress is a measure of the average amount of Force exerted per unit Area. Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature In Thermodynamics and Chemistry, chemical potential, symbolized by μ, is a term introduced by the American engineer chemist and mathematical The particle number, N, is the number of so called ' Elementary particles (or elementary constituents in a thermodynamical system. In Thermodynamics, entropy is a measure of how close a Thermodynamic system is to equilibrium In Thermodynamics, a thermodynamic system, originally called a working substance, is defined as that part of the universe that is under consideration In Thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium Mechanical equilibrium, and Probability is the likelihood or chance that something is the case or will happen In combinatorial mathematics, a combination is an un-ordered collection of distinct elements usually of a prescribed size and taken from a given set In Statistical mechanics, a microstate describes a specific detailed microscopic configuration of a system that the system visits in the course of its thermal fluctuations Statistical mechanics is the application of Probability theory, which includes mathematical tools for dealing with large populations to the field of Mechanics In the ice melting example, the difference in temperature between a warm room (the surroundings) and cold glass of ice and water (the system and not part of the room), begins to be equalized as portions of the heat energy from the warm surroundings spread out to the cooler system of ice and water.

Thermodynamic System
Thermodynamic System

Over time the temperature of the glass and its contents and the temperature of the room become equal. The entropy of the room has decreased as some of its energy has been dispersed to the ice and water. However, as calculated in the example, the entropy of the system of ice and water has increased more than the entropy of the surrounding room has decreased. In an isolated system such as the room and ice water taken together, the dispersal of energy from warmer to cooler always results in a net increase in entropy. In the Natural sciences an isolated system, as contrasted with a open system, is a Physical system that does not interact with its Surroundings Thus, when the 'universe' of the room and ice water system has reached a temperature equilibrium, the entropy change from the initial state is at a maximum. The entropy of the thermodynamic system is a measure of how far the equalization has progressed. In Thermodynamics, a thermodynamic system, originally called a working substance, is defined as that part of the universe that is under consideration

A special case of entropy increase, the entropy of mixing, occurs when two or more different substances are mixed. The entropy of mixing is the change in the Configuration entropy, an extensive thermodynamic quantity when two different Chemical substances If the substances are at the same temperature and pressure, there will be no net exchange of heat or work - the entropy increase will be entirely due to the mixing of the different substances. [11]

From a macroscopic perspective, in classical thermodynamics the entropy is interpreted simply as a state function of a thermodynamic system: that is, a property depending only on the current state of the system, independent of how that state came to be achieved. Classical thermodynamics is a branch of Physics developed in the nineteenth century by Sadi Carnot (1824 Emile Clapeyron (1834 Rudolf Clausius In Thermodynamics, a state function, state quantity, or a function of state, is a property of a system that depends only on the current In Thermodynamics, a thermodynamic system, originally called a working substance, is defined as that part of the universe that is under consideration The state function has the important property that, when multiplied by a reference temperature, it can be understood as a measure of the amount of energy in a physical system that cannot be used to do thermodynamic work; i. In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός In Thermodynamics, work is the quantity of Energy transferred from one system to another without an accompanying transfer of Entropy. e. , work mediated by thermal energy. More precisely, in any process where the system gives up energy ΔE, and its entropy falls by ΔS, a quantity at least TR ΔS of that energy must be given up to the system's surroundings as unusable heat (TR is the temperature of the system's external surroundings). In Physics, heat, symbolized by Q, is Energy transferred from one body or system to another due to a difference in Temperature Otherwise the process will not go forward.

In 1862, Clausius stated what he calls the “theorem respecting the equivalence-values of the transformations” or what is now known as the second law of thermodynamics, as such:

The algebraic sum of all the transformations occurring in a cyclical process can only be positive, or, as an extreme case, equal to nothing. The second law of Thermodynamics is an expression of the universal law of increasing Entropy, stating that the entropy of an Isolated system which

Quantitatively, Clausius states the mathematical expression for this theorem is as follows. Let δQ be an element of the heat given up by the body to any reservoir of heat during its own changes, heat which it may absorb from a reservoir being here reckoned as negative, and T the absolute temperature of the body at the moment of giving up this heat, then the equation:

\int \frac{\delta Q}{T} = 0

must be true for every reversible cyclical process, and the relation:

\int \frac{\delta Q}{T} \ge 0

must hold good for every cyclical process which is in any way possible. Thermodynamic temperature is the absolute measure of Temperature and is one of the principal parameters of Thermodynamics. This is the essential formulation of the second law and one of the original forms of the concept of entropy. It can be seen that the dimensions of entropy are energy divided by temperature, which is the same as the dimensions of Boltzmann's constant (kB) and heat capacity. Bridge from macroscopic to microscopic physics Boltzmann's constant k is a bridge between Macroscopic and microscopic physics Specific heat capacity, also known simply as specific heat, is the measure of the heat energy required to increase the Temperature of a unit quantity The SI unit of entropy is "joule per kelvin" (J·K−1). The joule (written in lower case ˈdʒuːl or /ˈdʒaʊl/ (symbol J) is the SI unit of Energy measuring heat, Electricity The kelvin (symbol K) is a unit increment of Temperature and is one of the seven SI base units The Kelvin scale is a thermodynamic In this manner, the quantity "ΔS" is utilized as a type of internal energy, which accounts for the effects of irreversibility, in the energy balance equation for any given system. In science a Process that is not reversible is called irreversible. In the Gibbs free energy equation, i. In Thermodynamics, the Gibbs free energy ( IUPAC recommended name Gibbs energy or Gibbs function) is a Thermodynamic potential which e. ΔG = ΔH - TΔS, for example, which is a formula commonly utilized to determine if chemical reactions will occur, the energy related to entropy changes TΔS is subtracted from the "total" system energy ΔH to give the "free" energy ΔG of the system, as during a chemical process or as when a system changes state. A chemical reaction is a process that always results in the interconversion of Chemical substances The substance or substances initially involved in a chemical reaction are called In a " scientific " sense a chemical process is a method or means of somehow changing one or more Chemicals or Chemical compounds Such a chemical

Microscopic definition of entropy (statistical mechanics)

Main article: Entropy (statistical thermodynamics)

In statistical thermodynamics the entropy is defined as (proportional to) the logarithm of the number of microscopic configurations that result in the observed macroscopic description of the thermodynamic system:

S = k_B \ln \Omega \!

where

kB is Boltzmann's constant 1. In Thermodynamics, statistical entropy is the modeling of the energetic function Entropy using Probability theory. In Thermodynamics, statistical thermodynamics is the study of the microscopic behaviors of Thermodynamic systems using Probability theory. In Mathematics, the logarithm of a number to a given base is the power or Exponent to which the base must be raised in order to produce In Statistical mechanics, a microstate describes a specific detailed microscopic configuration of a system that the system visits in the course of its thermal fluctuations Macroscopic is commonly used to describe physical objects that are measurable and observable by the Naked eye. Bridge from macroscopic to microscopic physics Boltzmann's constant k is a bridge between Macroscopic and microscopic physics 38066×10−23 J K−1 and
\Omega \! is the number of microstates corresponding to the observed thermodynamic macrostate. In Statistical mechanics, a microstate describes a specific detailed microscopic configuration of a system that the system visits in the course of its thermal fluctuations

This definition is considered to be the fundamental definition of entropy (as all other definitions can be mathematically derived from it, but not vice versa). In Boltzmann's 1896 Lectures on Gas Theory, he showed that this expression gives a measure of entropy for systems of atoms and molecules in the gas phase, thus providing a measure for the entropy of classical thermodynamics.

In 1877, Boltzmann visualized a probabilistic way to measure the entropy of an ensemble of ideal gas particles, in which he defined entropy to be proportional to the logarithm of the number of microstates such a gas could occupy. These four properties that constitute an ideal gas can be easily remembered by the acronym RIPE which stands for - R andom Motion (molecules are in constant random motion Henceforth, the essential problem in statistical thermodynamics, i. In Thermodynamics, statistical thermodynamics is the study of the microscopic behaviors of Thermodynamic systems using Probability theory. e. according to Erwin Schrödinger, has been to determine the distribution of a given amount of energy E over N identical systems.

Statistical mechanics explains entropy as the amount of uncertainty (or "mixedupness" in the phrase of Gibbs) which remains about a system, after its observable macroscopic properties have been taken into account. Statistical mechanics is the application of Probability theory, which includes mathematical tools for dealing with large populations to the field of Mechanics Josiah Willard Gibbs ( February 11, 1839 &ndash April 28, 1903) was an American theoretical Physicist, Chemist For a given set of macroscopic variables, like temperature and volume, the entropy measures the degree to which the probability of the system is spread out over different possible quantum states. The more states available to the system with higher probability, the greater the entropy. More specifically, entropy is a logarithmic measure of the density of states. Definition and base Logarithmic scales are either defined for ratios of the underlying quantity or one has to agree to measure In statistical and Condensed matter physics, the density of states ( DOS) of a system describes the number of states at each energy level that are available In essence, the most general interpretation of entropy is as a measure of our uncertainty about a system. The equilibrium state of a system maximizes the entropy because we have lost all information about the initial conditions except for the conserved variables; maximizing the entropy maximizes our ignorance about the details of the system. In Thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium Mechanical equilibrium, and [12] This uncertainty is not of the everyday subjective kind, but rather the uncertainty inherent to the experimental method and interpretative model.

On the molecular scale, the two definitions match up because adding heat to a system, which increases its classical thermodynamic entropy, also increases the system's thermal fluctuations, so giving an increased lack of information about the exact microscopic state of the system, i. Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature e. an increased statistical mechanical entropy.

The interpretative model has a central role in determining entropy. The qualifier "for a given set of macroscopic variables" above has very deep implications: if two observers use different sets of macroscopic variables, then they will observe different entropies. For example, if observer A uses the variables U, V and W, and observer B uses U, V, W, X, then, by changing X, observer B can cause an effect that looks like a violation of the second law of thermodynamics to observer A. In other words: the set of macroscopic variables one chooses must include everything that may change in the experiment, otherwise one might see decreasing entropy![13]

Entropy in chemical thermodynamics

Main article: Chemical thermodynamics

Thermodynamic entropy is central in chemical thermodynamics, enabling changes to be quantified and the outcome of reactions predicted. In Thermodynamics, chemical thermodynamics is the mathematical study of the interrelation of Heat and work with Chemical reactions or with a In Thermodynamics, chemical thermodynamics is the mathematical study of the interrelation of Heat and work with Chemical reactions or with a The second law of thermodynamics states that entropy in the combination of a system and its surroundings (or in an isolated system by itself) increases during all spontaneous chemical and physical processes. The second law of Thermodynamics is an expression of the universal law of increasing Entropy, stating that the entropy of an Isolated system which In the Natural sciences an isolated system, as contrasted with a open system, is a Physical system that does not interact with its Surroundings Spontaneity in chemistry means “by itself, or without any outside influence”, and has nothing to do with speed. The Clausius equation of δqrev/T = ΔS introduces the measurement of entropy change, ΔS. Entropy change describes the direction and quantitates the magnitude of simple changes such as heat transfer between systems – always from hotter to cooler spontaneously. In Physics, heat, symbolized by Q, is Energy transferred from one body or system to another due to a difference in Temperature [14] Thus, when a mole of substance at 0 K is warmed by its surroundings to 298 K, the sum of the incremental values of qrev/T constitute each element's or compound's standard molar entropy, a fundamental physical property and an indicator of the amount of energy stored by a substance at 298 K. The mole (symbol mol) is a unit of Amount of substance: it is an SI base unit, and almost the only unit to be used to measure this [15][16] Entropy change also measures the mixing of substances as a summation of their relative quantities in the final mixture. [17]

Entropy is equally essential in predicting the extent of complex chemical reactions, i. e. whether a process will go as written or proceed in the opposite direction. For such applications, ΔS must be incorporated in an expression that includes both the system and its surroundings, ΔSuniverse = ΔSsurroundings + ΔS system. This expression becomes, via some steps, the Gibbs free energy equation for reactants and products in the system: ΔG [the Gibbs free energy change of the system] = ΔH [the enthalpy change] −T ΔS [the entropy change]. In Thermodynamics, the Gibbs free energy ( IUPAC recommended name Gibbs energy or Gibbs function) is a Thermodynamic potential which In Thermodynamics, the Gibbs free energy ( IUPAC recommended name Gibbs energy or Gibbs function) is a Thermodynamic potential which In Thermodynamics and molecular chemistry, the enthalpy (denoted as H, h, or rarely as χ) is a quotient or description of [15]

The second law

Main article: Second law of thermodynamics

An important law of physics, the second law of thermodynamics, states that the total entropy of any isolated thermodynamic system tends to increase over time, approaching a maximum value; and so, by implication, the entropy of the universe (i. The second law of Thermodynamics is an expression of the universal law of increasing Entropy, stating that the entropy of an Isolated system which A physical law or scientific law is a Scientific generalization based on empirical Observations of physical behavior (i The second law of Thermodynamics is an expression of the universal law of increasing Entropy, stating that the entropy of an Isolated system which e. the system and its surroundings), assumed as an isolated system, tends to increase. Two important consequences are that heat cannot of itself pass from a colder to a hotter body: i. e. , it is impossible to transfer heat from a cold to a hot reservoir without at the same time converting a certain amount of work to heat. It is also impossible for any device that can operate on a cycle to receive heat from a single reservoir and produce a net amount of work; it can only get useful work out of the heat if heat is at the same time transferred from a hot to a cold reservoir. This means that there is no possibility of an isolated "perpetual motion" system. The term perpetual motion, taken literally refers to movement that goes on forever Also, from this it follows that a reduction in the increase of entropy in a specified process, such as a chemical reaction, means that it is energetically more efficient. A chemical reaction is a process that always results in the interconversion of Chemical substances The substance or substances initially involved in a chemical reaction are called

In general, according to the second law, the entropy of a system that is not isolated may decrease. An air conditioner, for example, cools the air in a room, thus reducing the entropy of the air. An air conditioner is an Appliance, System, or mechanism designed to extract Heat from an area via a Refrigeration cycle The heat, however, involved in operating the air conditioner always makes a bigger contribution to the entropy of the environment than the decrease of the entropy of the air. Thus the total entropy of the room and the environment increases, in agreement with the second law.

Entropy balance equation for open systems

In chemical engineering, the principles of thermodynamics are commonly applied to "open systems", i. Chemical engineering is the branch of Engineering that deals with the application of Physical science (e e. those in which heat, work, and mass flow across the system boundary. In Physics, heat, symbolized by Q, is Energy transferred from one body or system to another due to a difference in Temperature In Thermodynamics, work is the quantity of Energy transferred from one system to another without an accompanying transfer of Entropy. Mass is a fundamental concept in Physics, roughly corresponding to the Intuitive idea of how much Matter there is in an object In a system in which there are flows of both heat (\dot{Q}) and work, i. e. \dot{W}_S (shaft work) and P(dV/dt) (pressure-volume work), across the system boundaries, the heat flow, but not the work flow, causes a change in the entropy of the system. This rate of entropy change is \dot{Q}/T, where T is the absolute thermodynamic temperature of the system at the point of the heat flow. Thermodynamic temperature is the absolute measure of Temperature and is one of the principal parameters of Thermodynamics. If, in addition, there are mass flows across the system boundaries, the total entropy of the system will also change due to this convected flow.

During steady-state continuous operation, an entropy balance applied to an open system accounts for system entropy changes related to heat flow and mass flow across the system boundary.
During steady-state continuous operation, an entropy balance applied to an open system accounts for system entropy changes related to heat flow and mass flow across the system boundary. A Unit operation is considered to be at a steady state with respect to an operation variable if that variable does not change with time

To derive a generalized entropy balanced equation, we start with the general balance equation for the change in any extensive quantity Θ in a thermodynamic system, a quantity that may be either conserved, such as energy, or non-conserved, such as entropy. In the Physical sciences an intensive property (also called a bulk property) is a Physical property of a system that does not depend on the In Thermodynamics, a thermodynamic system, originally called a working substance, is defined as that part of the universe that is under consideration The basic generic balance expression states that dΘ/dt, i. e. the rate of change of Θ in the system, equals the rate at which Θ enters the system at the boundaries, minus the rate at which Θ leaves the system across the system boundaries, plus the rate at which Θ is generated within the system. Using this generic balance equation, with respect to the rate of change with time of the extensive quantity entropy S, the entropy balance equation for an open thermodynamic system is:[18]

\frac{dS}{dt} = \sum_{k=1}^K \dot{M}_k \hat{S}_k + \frac{\dot{Q}}{T} + \dot{S}_{gen}

where

\sum_{k=1}^K \dot{M}_k \hat{S}_k = the net rate of entropy flow due to the flows of mass into and out of the system (where \hat{S} = entropy per unit mass).
\frac{\dot{Q}}{T} = the rate of entropy flow due to the flow of heat across the system boundary.
\dot{S}_{gen} = the rate of internal generation of entropy within the system.

Note, also, that if there are multiple heat flows, the term \dot{Q}/T is to be replaced by \sum \dot{Q}_j/T_j, where \dot{Q}_j is the heat flow and Tj is the temperature at the jth heat flow port into the system.

Entropy in quantum mechanics (von Neumann entropy)

Main article: von Neumann entropy

In quantum statistical mechanics, the concept of entropy was developed by John von Neumann and is generally referred to as "von Neumann entropy". In Quantum statistical mechanics, von Neumann entropy refers to the extension of classical Entropy concepts to the field of Quantum mechanics. Quantum statistical mechanics is the study of Statistical ensembles of quantum mechanical systems. In Quantum statistical mechanics, von Neumann entropy refers to the extension of classical Entropy concepts to the field of Quantum mechanics. Von Neumann established a rigorous mathematical framework for quantum mechanics with his work Mathematische Grundlagen der Quantenmechanik. He provided in this work a theory of measurement, where the usual notion of wave collapse is described as an irreversible process (the so called von Neumann or projective measurement). Using this concept, in conjunction with the density matrix he extended the classical concept of entropy into the quantum domain.

It is well known that a Shannon based definition of information entropy leads in the classical case to the Boltzmann entropy. It is tempting to regard the Von Neumann entropy as the corresponding quantum mechanical definition. But the latter is problematic from quantum information point of view. Consequently Stotland, Pomeransky, Bachmat and Cohen have introduced a new definition of entropy that reflects the inherent uncertainty of quantum mechanical states. This definition allows to distinguish between the minimum uncertainty entropy of pure states, and the excess statistical entropy of mixtures. [19]

Entropy in Astrophysics

In astrophysics, what is referred to as "entropy" is actually the adiabatic constant derived as follows.

Using the first law of thermodynamics for a quasi-static, infinitesimal process for a hydrostatic system

dQ = dU − dW. In Physics, thermodynamics (from the Greek θερμη therme meaning " Heat " and δυναμις dynamis meaning "

For an ideal gas in this special case, the internal energy, U, is only a function of T; therefore the partial derivative of heat capacity with respect to T is identically the same as the full derivative, yielding through some manipulation

dQ = C_{V} dT+P\,dV.

Further manipulation using the differential version of the ideal gas law, the previous equation, and assuming constant pressure, one finds

dQ = C_{P} dT-V\,dP.

For an adiabatic process dQ = 0 and recalling \gamma = \frac{C_{P}}{C_{V}}, one finds

\frac{V\,dP = C_{P} dT}{P\,dV = -C_{V} dT}
\frac{dP}{P} = -\frac{dV}{V}\gamma.

One can solve this simple differential equation to find

PVγ = constant = K

This equation is known as an expression for the adiabatic constant, K, also called the adiabat. From the ideal gas equation one also knows

P=\frac{\rho k_{B}T}{\mu m_{H}},

where kB is Boltzmann's constant. Substituting this into the above equation along with V = [grams] / ρ and γ = 5 / 3 for an ideal monoatomic gas one finds

K = \frac{k_{B}T}{\mu m_{H} \rho^{2/3}},

where μ is the mean molecular weight of the gas or plasma; and mH is the mass of the Hydrogen atom, which is extremely close to the mass of the proton, mp, the quantity more often used in astrophysical theory of galaxy clusters. This is what astrophysicists refer to as "entropy" and has units of [keV cm2]. Famous Astronomers and Astrophysicists include A Marc Aaronson ( USA, 1950 &ndash 1987 This quantity relates to the thermodynamic entropy as

S = kBlnΩ + S0

where Ω, the density of states in statistical theory, takes on the value of K as defined above.

Standard textbook definitions

The following is a list of definitions of entropy from a collection of textbooks. Note that textbook definitions are not always the most helpful definitions, but they are an important aspect of the culture surrounding the concept of entropy.

Approaches to understanding entropy

Order and disorder

Main article: Entropy (order and disorder)

Entropy, historically, has often been associated with the amount of order, disorder, and/or chaos in a thermodynamic system. In thermodynamics Entropy is often associated with the amount of Order, disorder and/or Chaos in a Thermodynamic system. Randomness is a lack of order Purpose, cause, or predictability Chaos (derived from the Ancient Greek, Chaos) typically refers to Unpredictability, and is the antithesis of Cosmos. In Thermodynamics, a thermodynamic system, originally called a working substance, is defined as that part of the universe that is under consideration The traditional definition of entropy is that it refers to changes in the status quo of the system and is a measure of "molecular disorder" and the amount of wasted energy in a dynamical energy transformation from one state or form to another. [31] In this direction, a number of authors, in recent years, have derived exact entropy formulas to account for and measure disorder and order in atomic and molecular assemblies. [32][9][33][34] One of the simpler entropy order/disorder formulas is that derived in 1984 by thermodynamic physicist Peter Landsberg, which is based on a combination of thermodynamics and information theory arguments. In Physics, thermodynamics (from the Greek θερμη therme meaning " Heat " and δυναμις dynamis meaning " Information theory is a branch of Applied mathematics and Electrical engineering involving the quantification of Information. Landsberg argues that when constraints operate on a system, such that it is prevented from entering one or more of its possible or permitted states, as contrasted with its forbidden states, the measure of the total amount of “disorder” in the system is given by the following expression:[33][34]

Disorder=C_D/C_I\,

Similarly, the total amount of "order" in the system is given by:

Order=1-C_O/C_I\,

In which CD is the "disorder" capacity of the system, which is the entropy of the parts contained in the permitted ensemble, CI is the "information" capacity of the system, an expression similar to Shannon's channel capacity, and CO is the "order" capacity of the system. In Electrical engineering, Computer science and Information theory, channel capacity is the tightest upper bound on the amount of Information [9]

Energy dispersal

Main article: Entropy (energy dispersal)

The concept of entropy can be described qualitatively as a measure of energy dispersal at a specific temperature. The thermodynamic concept of entropy can be described qualitatively as a measure of energy dispersal (energy distribution at a specific temperature [35] Similar terms have been in use from early in the history of classical thermodynamics, and with the development of statistical thermodynamics and quantum theory, entropy changes have been described in terms of the mixing or "spreading" of the total energy of each constituent of a system over its particular quantized energy levels. Classical thermodynamics is a branch of Physics developed in the nineteenth century by Sadi Carnot (1824 Emile Clapeyron (1834 Rudolf Clausius In Thermodynamics, statistical thermodynamics is the study of the microscopic behaviors of Thermodynamic systems using Probability theory. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons

Ambiguities in the terms disorder and chaos, which usually have meanings directly opposed to equilibrium, contribute to widespread confusion and hamper comprehension of entropy for most students. [36] As the second law of thermodynamics shows, in an isolated system internal portions at different temperatures will tend to adjust to a single uniform temperature and thus produce equilibrium. The second law of Thermodynamics is an expression of the universal law of increasing Entropy, stating that the entropy of an Isolated system which In the Natural sciences an isolated system, as contrasted with a open system, is a Physical system that does not interact with its Surroundings A recently developed educational approach avoids ambiguous terms and describes such spreading out of energy as dispersal, which leads to loss of the differentials required for work even though the total energy remains constant in accordance with the first law of thermodynamics. In Thermodynamics, the first law of thermodynamics is an expression of the more universal physical law of the Conservation of energy. [37] Physical chemist Peter Atkins, for example, who previously wrote of dispersal leading to a disordered state, now writes that "spontaneous changes are always accompanied by a dispersal of energy", and has discarded 'disorder' as a description. Peter William Atkins (born August 10, 1940) is an English Chemist and a Fellow and Professor of Chemistry [38][14]

Entropy and Information theory

Main articles: Information entropy and Entropy in thermodynamics and information theory

In information theory, entropy is the measure of the amount of information that is missing before reception and is sometimes referred to as Shannon entropy. There are close parallels between the mathematical expressions for the thermodynamic Entropy, usually denoted by S, of a physical system in the Statistical thermodynamics Information theory is a branch of Applied mathematics and Electrical engineering involving the quantification of Information. [39] Shannon entropy is a broad and general concept which finds applications in information theory as well as thermodynamics. Information theory is a branch of Applied mathematics and Electrical engineering involving the quantification of Information. In Physics the Maximum entropy school of thermodynamics (or more colloquially the MaxEnt school of thermodynamics initiated with two papers published in the Physical It was originally devised by Claude Shannon in 1948 to study the amount of information in a transmitted message. Claude Elwood Shannon (April 30 1916 – February 24 2001 an American Electronic engineer and Mathematician, is "the father of Information The definition of the information entropy is, however, quite general, and is expressed in terms of a discrete set of probabilities pi. In the case of transmitted messages, these probabilities were the probabilities that a particular message was actually transmitted, and the entropy of the message system was a measure of how much information was in the message. For the case of equal probabilities (i. e. each message is equally probable), the Shannon entropy (in bits) is just the number of yes/no questions needed to determine the content of the message.

The question of the link between information entropy and thermodynamic entropy is a hotly debated topic. Some authors argue that there is a link between the two,[40][41][42] while others will argue that they have absolutely nothing to do with each other. [43]

The expressions for the two entropies are very similar. The information entropy H for equal probabilities pi = p is:

H=K\ln(1/p)\,

where K is a constant which determines the units of entropy. For example, if the units are bits, then K=1/ln(2). The thermodynamic entropy S , from a statistical mechanical point of view was first expressed by Boltzmann:

S=k\ln(1/p)\,

where p  is the probability of a system being in a particular microstate, given that it is in a particular macrostate, and k  is Boltzmann's constant. It can be seen that one may think of the thermodynamic entropy as Boltzmann's constant, divided by ln(2), times the number of yes/no questions that must be asked in order to determine the microstate of the system, given that we know the macrostate. The link between thermodynamic and information entropy was developed in a series of papers by Edwin Jaynes beginning in 1957. Edwin Thompson Jaynes ( July 5, 1922 &ndash April 30, 1998) was Wayman Crow Distinguished Professor of Physics at Washington University [44]

The problem with linking thermodynamic entropy to information entropy is that in information entropy the entire body of thermodynamics which deals with the physical nature of entropy is missing. The second law of thermodynamics which governs the behavior of thermodynamic systems in equilibrium, and the first law which expresses heat energy as the product of temperature and entropy are physical concepts rather than informational concepts. If thermodynamic entropy is seen as including all of the physical dynamics of entropy as well as the equilibrium statistical aspects, then information entropy gives only part of the description of thermodynamic entropy. Some authors, like Tom Schneider, argue for dropping the word entropy for the H function of information theory and using Shannon's other term "uncertainty" instead. [45]

Ice melting example

Main article: disgregation

The illustration for this article is a classic example in which entropy increases in a small 'universe', a thermodynamic system consisting of the 'surroundings' (the warm room) and 'system' (glass, ice, cold water). In the History of thermodynamics, disgregation was defined in 1862 by Rudolf Clausius as the magnitude of the degree in which the molecules of a body are separated In Thermodynamics, a thermodynamic system, originally called a working substance, is defined as that part of the universe that is under consideration In this universe, some heat energy δQ from the warmer room surroundings (at 298 K or 25 °C) will spread out to the cooler system of ice and water at its constant temperature T of 273 K (0 °C), the melting temperature of ice. In Physics, heat, symbolized by Q, is Energy transferred from one body or system to another due to a difference in Temperature The entropy of the system will change by the amount dS = δQ/T, in this example δQ/273 K. (The heat δQ for this process is the energy required to change water from the solid state to the liquid state, and is called the enthalpy of fusion, i. The standard Enthalpy of fusion (symbol \Delta{}H_{fus} also known as the heat of fusion or specific melting heat, is the amount of e. the ΔH for ice fusion. ) The entropy of the surroundings will change by an amount dS = −δQ/298 K. So in this example, the entropy of the system increases, whereas the entropy of the surroundings decreases.

It is important to realize that the decrease in the entropy of the surrounding room is less than the increase in the entropy of the ice and water: the room temperature of 298 K is larger than 273 K and therefore the ratio, (entropy change), of δQ/298 K for the surroundings is smaller than the ratio (entropy change), of δQ/273 K for the ice+water system. To find the entropy change of our "universe", we add up the entropy changes for its constituents: the surrounding room, and the ice+water. The total entropy change is positive; this is always true in spontaneous events in a thermodynamic system and it shows the predictive importance of entropy: the final net entropy after such an event is always greater than was the initial entropy. In Thermodynamics, a thermodynamic system, originally called a working substance, is defined as that part of the universe that is under consideration

As the temperature of the cool water rises to that of the room and the room further cools imperceptibly, the sum of the δQ/T over the continuous range, at many increments, in the initially cool to finally warm water can be found by calculus. The entire miniature "universe", i. e. this thermodynamic system, has increased in entropy. Energy has spontaneously become more dispersed and spread out in that "universe" than when the glass of ice water was introduced and became a "system" within it.

Topics in entropy

Entropy and life

Main article: Entropy and life

For over a century and a half, beginning with Clausius' 1863 memoir "On the Concentration of Rays of Heat and Light, and on the Limits of its Action", much writing and research has been devoted to the relationship between thermodynamic entropy and the evolution of life. Much writing has been devoted to Entropy and life. Research concerning the relationship between the thermodynamic quantity Entropy and the Evolution of Life eVolution is the third Album by eLDee, it was due to be released in 2008 Life is a state that distinguishes Organisms from non-living objects such as non-life and dead organisms being manifested by growth through Metabolism The argument that life feeds on negative entropy or negentropy as put forth in the 1944 book What is Life? by physicist Erwin Schrödinger served as a further stimulus to this research. Negative Entropy or negentropy or syntropy of a living system is the entropy that it exports to maintain its own entropy low (see Entropy and life What is Life? with Mind and Matter is a non-fiction book on science for the lay reader written by physicist Erwin Schrödinger. A physicist is a Scientist who studies or practices Physics. Physicists study a wide range of physical phenomena in many branches of physics spanning Recent writings have utilized the concept of Gibbs free energy to elaborate on this issue. In Thermodynamics, the Gibbs free energy ( IUPAC recommended name Gibbs energy or Gibbs function) is a Thermodynamic potential which Tangentially, some creationists have argued that entropy rules out evolution. eVolution is the third Album by eLDee, it was due to be released in 2008 [46]

In the popular 1982 textbook Principles of Biochemistry by noted American biochemist Albert Lehninger, for example, it is argued that the order produced within cells as they grow and divide is more than compensated for by the disorder they create in their surroundings in the course of growth and division. Albert Lester Lehninger ( February 17, 1917 – March 4, 1986) was an American Biochemist, and is widely regarded as a pioneer In short, according to Lehninger, "living organisms preserve their internal order by taking from their surroundings free energy, in the form of nutrients or sunlight, and returning to their surroundings an equal amount of energy as heat and entropy. In Thermodynamics, the term thermodynamic free energy refers to the amount of work that can be extracted from a System, and is helpful in Engineering In Physics, heat, symbolized by Q, is Energy transferred from one body or system to another due to a difference in Temperature "[47]

Evolution related definitions:

The arrow of time

Main article: Entropy (arrow of time)

Entropy is the only quantity in the physical sciences that "picks" a particular direction for time, sometimes called an arrow of time. Entropy is the only quantity in the physical sciences that "picks" a particular direction for time sometimes called an Arrow of time. As we go "forward" in time, the Second Law of Thermodynamics tells us that the entropy of an isolated system can only increase or remain the same; it cannot decrease. In the Natural sciences an isolated system, as contrasted with a open system, is a Physical system that does not interact with its Surroundings Hence, from one perspective, entropy measurement is thought of as a kind of clock.

Entropy and cosmology

Main article: Black hole thermodynamics

As a finite universe may be considered an isolated system, it may be subject to the Second Law of Thermodynamics, so that its total entropy is constantly increasing. In Physics, black hole thermodynamics is the area of study that seeks to reconcile the Laws of thermodynamics with the existence of Black hole Event It has been speculated that the universe is fated to a heat death in which all the energy ends up as a homogeneous distribution of thermal energy, so that no more work can be extracted from any source. The heat death is a possible final state of the universe, in which it has " run down " to a state of no Thermodynamic free energy to sustain In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός

If the universe can be considered to have generally increasing entropy, then - as Roger Penrose has pointed out - gravity plays an important role in the increase because gravity causes dispersed matter to accumulate into stars, which collapse eventually into black holes. Sir Roger Penrose, PhD, OM, FRS (born 8 August 1931) is an English Mathematical physicist and Emeritus Gravitation is a natural Phenomenon by which objects with Mass attract one another A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e Jacob Bekenstein and Stephen Hawking have shown that black holes have the maximum possible entropy of any object of equal size. Jacob David Bekenstein (born May 1, 1947) is a Physicist who has contributed to the foundation of Black hole thermodynamics and to other aspects Stephen William Hawking CH, CBE, FRS, FRSA (born 8 January 1942 is a British theoretical physicist. This makes them likely end points of all entropy-increasing processes, if they are totally effective matter and energy traps. Hawking has, however, recently changed his stance on this aspect.

The role of entropy in cosmology remains a controversial subject. Recent work has cast extensive doubt on the heat death hypothesis and the applicability of any simple thermodynamic model to the universe in general. Although entropy does increase in the model of an expanding universe, the maximum possible entropy rises much more rapidly - thus entropy density is decreasing with time. This results in an "entropy gap" pushing the system further away from equilibrium. Other complicating factors, such as the energy density of the vacuum and macroscopic quantum effects, are difficult to reconcile with thermodynamical models, making any predictions of large-scale thermodynamics extremely difficult. Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons

Miscellaneous definitions

Other relations

Other mathematical definitions

Sociological definitions

The concept of entropy has also entered the domain of sociology, generally as a metaphor for chaos, disorder or dissipation of energy, rather than as a direct measure of thermodynamic or information entropy:

Quotes

“ Any method involving the notion of entropy, the very existence of which depends on the second law of thermodynamics, will doubtless seem to many far-fetched, and may repel beginners as obscure and difficult of comprehension. The second law of Thermodynamics is an expression of the universal law of increasing Entropy, stating that the entropy of an Isolated system which ”
--Willard Gibbs, Graphical Methods in the Thermodynamics of Fluids (1873)
“ My greatest concern was what to call it. Josiah Willard Gibbs ( February 11, 1839 &ndash April 28, 1903) was an American theoretical Physicist, Chemist I thought of calling it ‘information’, but the word was overly used, so I decided to call it ‘uncertainty’. When I discussed it with John von Neumann, he had a better idea. Von Neumann told me, ‘You should call it entropy, for two reasons. In the first place your uncertainty function has been used in statistical mechanics under that name, so it already has a name. Statistical mechanics is the application of Probability theory, which includes mathematical tools for dealing with large populations to the field of Mechanics In the second place, and more important, nobody knows what entropy really is, so in a debate you will always have the advantage. ”
--Conversation between Claude Shannon and John von Neumann regarding what name to give to the “measure of uncertainty” or attenuation in phone-line signals (1949)

See also

References

  1. ^ Note: In certain types of advanced system configurations, such as at the critical point of water or when salt is added to an ice-water mixture, entropy can either increase or decrease depending on system parameters, such as temperature and pressure. Claude Elwood Shannon (April 30 1916 – February 24 2001 an American Electronic engineer and Mathematician, is "the father of Information Autocatalytic reactions are Chemical reactions in which at least one of the products is also a Reactant. The Brownian ratchet is a Thought experiment about an apparent Perpetual motion machine conceived by Richard Feynman in a Physics lecture at In Mathematics, chaos theory describes the behavior of certain dynamical systems – that is systems whose state evolves with time – that may exhibit dynamics that Configuration entropy is the Entropy associated with the geometric configuration of individual components comprising a distributed physical system In Thermodynamics, a departure function is defined for any thermodynamic property as the difference between the property as computed for an ideal gas and the property of the In Thermodynamics and molecular chemistry, the enthalpy (denoted as H, h, or rarely as χ) is a quotient or description of Entropy A New World View is a non-fiction book by Jeremy Rifkin and Ted Howard, with an Afterword by Nicholas Georgescu-Roegen. The entropy rate of a Stochastic process is informally the time density of the average information in a stochastic process Geometrical frustration and ice-rules The word Frustration was introduced to describe the situation where a system cannot simultaneously minimize the interaction Thermodynamic Entropy provides a measure of certain aspects of Energy in relation to Absolute temperature. Maxwell's demon was an 1867 Thought experiment by the Scottish Physicist James Clerk Maxwell, meant to raise questions about the possibility The multiplicity function for a two state paramagnet Ω(nN is the number of spin states such that n of the N spins point in the z-direction Statistical mechanics is the application of Probability theory, which includes mathematical tools for dealing with large populations to the field of Mechanics In Mathematics, Stirling's approximation (or Stirling's formula) is an approximation for large Factorials It is named in honour of James Stirling Thermodynamic databases contain information about thermodynamic properties for substances the most important being Enthalpy, Entropy, and A thermodynamic potential is a Scalar potential function used to represent the Thermodynamic state of a system. In Physical chemistry, Thermodynamics, Chemistry and Condensed matter physics, a critical point, also called a critical state For example, if the spontaneous crystallization of a supercooled liquid takes place under adiabatic conditions the entropy of the resulting crystal will be greater than that of the supercooled liquid (Denbigh, K. (1982). The Principles of Chemical Equilibrium, 4th Ed. ). In general, however, when ice melts, the entropy of the two adjoined systems, i. e. the adjacent hot and cold bodies, when thought of as one "universe", increases. Here are some further tutorials: Ice-melting – JCE example; Ice-melting and Entropy Change – example; Ice-melting and Entropy Change – discussions
  2. ^ Clausius, Rudolf (1862). Communicated to the Naturforschende Gesellschaft of Zurich, Jan. 27th, 1862; published in the Vierteljahrschrift of this Society, vol. vii. P. 48; in Poggendorff’s Annalen, May 1862, vol. cxvi. p. 73; in the Philosophical Magazine, S. 4. vol. xxiv. pp. 81, 201; and in the Journal des Mathematiques of Paris, S. 2. vol. vii. P. 209.
  3. ^ Daintith, John (2005). Oxford Dictionary of Physics. Oxford University Press. ISBN 0-19-280628-9.  
  4. ^ More explicitly, an energy TRS is not available to do useful work, where TR is the temperature of the coldest accessible reservoir or heat sink external to the system. For further discussion, see Exergy
  5. ^ a b Perrot, Pierre (1998). "Available energy" redirects here For the meaning of the term in particle collisions see Available energy (particle collision. A to Z of Thermodynamics. Oxford University Press. ISBN 0-19-856552-6.  
  6. ^ a b Clausius, Rudolf (1850). On the Motive Power of Heat, and on the Laws which can be deduced from it for the Theory of Heat. Poggendorff's Annalen der Physick, LXXIX (Dover Reprint). ISBN 0-486-59065-8.  
  7. ^ Avery, John (2003). Information Theory and Evolution. World Scientific. ISBN 981-238-399-9.  
  8. ^ Yockey, Hubert, P. (2005). Information Theory, Evolution, and the Origin of Life. . Cambridge University Press. ISBN 0-521-80293-8.  
  9. ^ a b c Brooks, Daniel, R. ; Wiley, E. O. (1988). Entropy as Evolution – Towards a Unified Theory of Biology. University of Chicago Press. ISBN 0-226-07574-5.  
  10. ^ McCulloch, Richard, S. (1876). Treatise on the Mechanical Theory of Heat and its Applications to the Steam-Engine, etc. . D. Van Nostrand.  
  11. ^ See, e. g. , Notes for a “Conversation About Entropy” for a brief discussion of both thermodynamic and "configurational" ("positional") entropy in chemistry.
  12. ^ EntropyOrderParametersComplexity.pdf
  13. ^ Jaynes, E. T., "The Gibbs Paradox," In Maximum Entropy and Bayesian Methods; Smith, C. R.; Erickson, G. J.; Neudorfer, P. O., Eds.; Kluwer Academic: Dordrecht, 1992, p.1-22
  14. ^ a b Atkins, Peter; Julio De Paula (2006). Physical Chemistry , 8th edition. Oxford University Press. ISBN 0-19-870072-5.  
  15. ^ a b Moore, J. W. ; C. L. Stanistski, P. C. Jurs (2005). Chemistry, The Molecular Science ,. Brooks Cole. ISBN 0-534-42201-2.  
  16. ^ Jungermann, A. H. (2006). “Entropy and the Shelf Model: A Quantum Physical Approach to a Physical Property”. Journal of Chemical Education 83: 1686-1694
  17. ^ Levine, I. N. (2002). Physical Chemistry, 5th edition. McGraw-Hill. ISBN 0-07-231808-2.  
  18. ^ Sandler, Stanley, I. (1989). Chemical and Engineering Thermodynamics. John Wiley & Sons. ISBN 0-471-83050-X.  
  19. ^ The information entropy of quantum mechanical states, Europhysics Letters 67, 700 (2004)
  20. ^ de Rosnay, Joel (1979). The Macroscope – a New World View (written by an M.I.T.-trained biochemist). Harper & Row, Publishers. ISBN 0-06-011029-5.  
  21. ^ Baierlein, Ralph (2003). Thermal Physics. Cambridge University Press. ISBN 0-521-65838-1.  
  22. ^ Schroeder, Daniel, R. (2000). Thermal Physics. New York: Addison Wesley Longman. ISBN 0-201-38027-7.  
  23. ^ McGraw-Hill Concise Encyclopedia of Chemistry, 2004
  24. ^ Chang, Raymond (1998). Chemistry, 6th Ed. . New York: McGraw Hill. ISBN 0-07-115221-0.  
  25. ^ Atkins, Peter; Julio De Paula (2006). Physical Chemistry , 8th edition. Oxford University Press. ISBN 0-19-870072-5.  
  26. ^ Cutnell, John, D. ; Johnson, Kenneth, J. (1998). Physics, 4th edition. John Wiley and Sons, Inc. . ISBN 0-471-19113-2.  
  27. ^ Haynie, Donald, T. (2001). Biological Thermodynamics. Cambridge University Press. ISBN 0-521-79165-0.  
  28. ^ Oxford Dictionary of Science, 2005
  29. ^ Barnes & Noble's Essential Dictionary of Science, 2004
  30. ^ Gribbin's Encyclopedia of Particle Physics, 2000
  31. ^ a b Haddad, Wassim M. ; Chellaboina, VijaySekhar; Nersesov, Sergey G. (2005). Thermodynamics - A Dynamical Systems Approach. Princeton University Press. ISBN 0-691-12327-6.  
  32. ^ Callen, Herbert, B (2001). Thermodynamics and an Introduction to Thermostatistics, 2nd Ed. . John Wiley and Sons. ISBN 0-471-86256-8.  
  33. ^ a b Landsberg, P. T. (1984). “Is Equilibrium always an Entropy Maximum?” J. Stat. Physics 35: 159-69.
  34. ^ a b Landsberg, P. T. (1984). “Can Entropy and “Order” Increase Together?” Physics Letters 102A:171-173
  35. ^ Frank L. Lambert, A Student’s Approach to the Second Law and Entropy
  36. ^ Carson, E. M. and J. R. Watson (Department of Educational and Professional Studies, Kings College, London), Undergraduate students' understandings of entropy and Gibbs Free energy, University Chemistry Education - 2002 Papers, Royal Society of Chemistry.
  37. ^ Frank L. Lambert, JCE 2002 (79) 187 [Feb Disorder--A Cracked Crutch for Supporting Entropy Discussions]
  38. ^ Atkins, Peter (1984). The Second Law. Scientific American Library. ISBN 0-7167-5004-X.  
  39. ^ Balian, Roger (2003). Entropy – Protean Concept (PDF). Poincaré Seminar 2: 119-45.
  40. ^ Brillouin, Leon (1956). Science and Information Theory. name. ISBN 0-486-43918-6.  
  41. ^ Georgescu-Roegen, Nicholas (1971). The Entropy Law and the Economic Process. Harvard University Press. ISBN 0-674-25781-2.  
  42. ^ Chen, Jing (2005). The Physical Foundation of Economics - an Analytical Thermodynamic Theory. World Scientific. ISBN 981-256-323-7.  
  43. ^ Lin, Shu-Kun. (1999). “Diversity and Entropy. ” Entropy (Journal), 1[1], 1-3.
  44. ^ Edwin T. Jaynes - Bibliography
  45. ^ Schneider, Tom, DELILA system (Deoxyribonucleic acid Library Language), (Information Theory Analysis of binding sites), Laboratory of Mathematical Biology, National Cancer Institute, FCRDC Bldg. 469. Rm 144, P. O. Box. B Frederick, MD 21702-1201, USA.
  46. ^ Entropy, Disorder and Life
  47. ^ Lehninger, Albert (1993). Principles of Biochemistry, 2nd Ed. . Worth Publishers. ISBN 0-87901-711-2.  
  48. ^ Schrödinger, Erwin (1944). What is Life - the Physical Aspect of the Living Cell. Cambridge University Press. ISBN 0-521-42708-8.  
  49. ^ von Baeyer, Christian, H. (2003). Information - the New Language of Science. Harvard University Press. ISBN 0-674-01387-5.  
  50. ^ Serway, Raymond, A. (1992). Physics for Scientists and Engineers. Saunders Golden Subburst Series. ISBN 0-03-096026-6.  
  51. ^ Example: "Entropology, not anthropology, should be the word for the discipline that devotes itself to the study of the process of disintegration in its most evolved forms. " (In A World on Wane, London, 1961, pg. 397; translated by John Russell of Tristes Tropiques by Claude Levi-Strauss. Claude Lévi-Strauss (klod levi stʁos born 28 November 1908 is a French Anthropologist. )
  52. ^ Hall, Calvin S. ; Nordby, Vernon J. (1999). A Primer of Jungian Psychology. New York: Meridian. ISBN 0-452-01186-8.  
  53. ^ Georgescu-Roegen, Nicholas (1971). The Entropy Law and the Economic Process. Harvard University Press. ISBN 0-674-25781-2.  
  54. ^ Burley, Peter; Foster, John (1994). Economics and Thermodynamics – New Perspectives on Economic Analysis. Kluwer Academic Publishers. ISBN 0-7923-9446-1.  
  55. ^ Bailey, Kenneth, D. (1990). Social Entropy Theory. State University of New York Press. ISBN 0-7914-0056-5.  
  56. ^ DeMarco, Tom; Lister, Timothy (1999). Peopleware - Productive Projects and Teams, 2nd. Ed. . Dorset House Publishing Co. . ISBN 0-932633-43-9.  

Further reading

  1. Ben-Naim, Arieh (2007). Entropy Demystified. World Scientific. ISBN 981-270-055-2.  
  2. Dugdale, J. S. (1996). Entropy and its Physical Meaning, 2nd Ed. , Taylor and Francis (UK); CRC (US). ISBN 0748405690.  
  3. Fermi, Enrico (1937). Thermodynamics. Prentice Hall. ISBN 0-486-60361-X.  
  4. Kroemer, Herbert; Charles Kittel (1980). Thermal Physics, 2nd Ed. , W. H. Freeman Company. ISBN 0-7167-1088-9.  
  5. Penrose, Roger (2005). Sir Roger Penrose, PhD, OM, FRS (born 8 August 1931) is an English Mathematical physicist and Emeritus The Road to Reality : A Complete Guide to the Laws of the Universe. ISBN 0-679-45443-8.  
  6. Reif, F. (1965). Fundamentals of statistical and thermal physics. McGraw-Hill. ISBN 0-07-051800-9.  
  7. Goldstein, Martin; Inge, F (1993). The Refrigerator and the Universe. Harvard University Press. ISBN 0-674-75325-9.  
  8. vonBaeyer; Hans Christian (1998). Maxwell's Demon: Why Warmth Disperses and Time Passes. Random House. ISBN 0-679-43342-2.  

External links

Dictionary

entropy

-noun

  1. (thermodynamics, countable)
  2. # strictly thermodynamic entropy. A measure of the amount of energy in a physical system which cannot be used to do mechanical work.
  3. # A measure of the disorder present in a system (now becoming obsolete in chemistry [1]).
  4. # The capacity factor for thermal energy that is hidden with respect to temperature [2].
  5. # The dispersal of energy; how much energy is spread out in a process, or how widely spread out it becomes, at a specific temperature. [3]
  6. (statistics, information theory, countable) A measure of the amount of information and noise present in a signal.
  7. (uncountable) The tendency of a system that is left to itself to descend into chaos.
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