Ludwig Boltzmann
Ludwig Eduard Boltzmann (1844-1906)
Born	February 20, 1844(1844-02-20) Vienna, Austrian Empire
Died	September 5, 1906 (aged 62) Duino near Trieste, Italy (at that time Austrian Empire)
Residence	Austria, Germany
Nationality	Austrian
Fields	Physicist
Institutions	University of Graz University of Vienna University of Munich University of Leipzig
Alma mater	University of Vienna
Doctoral advisor	Josef Stefan
Doctoral students	Paul Ehrenfest Philipp Frank Gustav Herglotz Lise Meitner
Known for	Boltzmann's constant Boltzmann equation Boltzmann distribution Stefan-Boltzmann law
Signature

Ludwig Eduard Boltzmann (February 20, 1844 – September 5, 1906) was an Austrian physicist famous for his founding contributions in the fields of statistical mechanics and statistical thermodynamics. Events 1472 - Orkney and Shetland are left by Norway to Scotland, due to a Dowry payment Year 1844 ( MDCCCXLIV) was a Leap year starting on Monday (link will display the full calendar of the Gregorian Calendar (or a Leap year Events 1590 - Alexander Farnese 's army forces Henry IV of France to raise the siege of Paris. Year 1906 ( MCMVI) was a Common year starting on Monday (link will display full calendar of the Gregorian calendar (or a Common year starting Austria (Österreich ( officially the Republic of Austria (Republik Österreich A physicist is a Scientist who studies or practices Physics. Physicists study a wide range of physical phenomena in many branches of physics spanning Statistical mechanics is the application of Probability theory, which includes mathematical tools for dealing with large populations to the field of Mechanics In Thermodynamics, statistical thermodynamics is the study of the microscopic behaviors of Thermodynamic systems using Probability theory. He was one of the most important advocates for atomic theory when that scientific model was still highly controversial. This article focuses on the historical models of the atom For a history of the study of how atoms combine to form molecules see History of the molecule.

Biography

Childhood and education

Boltzmann was born in Vienna, then capital of the Austrian Empire. For the history of these states before 1804 see Holy Roman Empire, Habsburg Monarchy, and articles on each of the component countries. His father, Ludwig George Boltzmann, was a tax official. His grandfather, who had moved to Vienna from Berlin, was a clock manufacturer, and Boltzmann’s mother, Katharina Pauernfeind, was originally from Salzburg. Berlin is the capital city and one of sixteen states of Germany. is the fourth-largest city in Austria and the capital of the federal state of Salzburg. He received his primary education from a private tutor at the home of his parents. Boltzmann attended high school in Linz, Upper Austria. Linz is the third largest city of Austria and capital of the state of Upper Austria (Oberösterreich Upper Austria (Oberösterreich Horní Rakousko is one of the nine states or Bundesländer of Austria. At age 15, Boltzmann lost his father.

Boltzmann studied physics at the University of Vienna, starting in 1863. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. The University of Vienna (Universität Wien is a Public university located in Vienna, Austria. Among his teachers were Josef Loschmidt, Joseph Stefan, Andreas von Ettingshausen and Jozef Petzval. Jan or Johann Josef Loschmidt ( March 15 1821 - July 8 1895) who referred to himself mostly as 'Josef' (omitting his first name Joseph Stefan ( Jožef Stefan) ( March 24, 1835 &ndash January 7, 1893) was a Physicist, Mathematician and Andreas Freiherr von Ettingshausen (born 25 November, 1796, Heidelberg and died 25 May, 1878, Vienna) was a German Joseph Petzval (Josef Maximilian Petzval Petzvál József Miksa Jozef Maximilián Petzval ( January 6, 1807 &ndash September 19, 1891) was Boltzmann received his PhD degree in 1866 working under the supervision of Stefan; his dissertation was on kinetic theory of gases. Year 1866 ( MDCCCLXVI) was a Common year starting on Monday (link will display the full calendar of the Gregorian calendar (or a Common In 1867 he became a Privatdozent (lecturer). Private docent (abbreviates PD or Priv-Doz) is a title conferred in some European university systems especially in German -speaking countries After obtaining his doctorate degree, Boltzmann worked two more years as Stefan’s assistant. It was Stefan who introduced Boltzmann to Maxwell's work. James Clerk Maxwell (13 June 1831 &ndash 5 November 1879 was a Scottish mathematician and theoretical physicist.

Academic career

In 1869, at age 25, he was appointed full Professor of Mathematical Physics at the University of Graz in the province of Styria. Year 1869 ( MDCCCLXIX) is a Common year starting on Friday (link will display the full calendar of the Gregorian calendar (or a Common year The University of Graz ( German, Karl-Franzens-Universität Graz) a University located in Graz, Austria, is the second-largest Styria (Steiermark is a state or Bundesland, located in the southeast of Austria. In 1869 he spent several months in Heidelberg working with Robert Bunsen and Leo Königsberger and then in 1871 he was with Gustav Kirchhoff and Hermann von Helmholtz in Berlin. Year 1869 ( MDCCCLXIX) is a Common year starting on Friday (link will display the full calendar of the Gregorian calendar (or a Common year Heidelberg is a city in Baden-Württemberg, Germany. As of 2006 over 140000 people live within the city's area Robert Wilhelm Eberhard Bunsen (31 March 1811 &ndash 16 August 1899 was a German Chemist. Leo Königsberger ( October 15, 1837 – December 15, 1921) was a German mathematician and historian of science. Gustav Robert Kirchhoff ( March 12, 1824 &ndash October 17, 1887) was a German Physicist who contributed to the fundamental In 1873 Boltzmann joined the University of Vienna as Professor of Mathematics and there he stayed until 1876. Year 1873 ( MDCCCLXXIII) was a Common year starting on Wednesday (link will display the full calendar of the Gregorian calendar (or a Common The University of Vienna (Universität Wien is a Public university located in Vienna, Austria. Year 1876 ( MDCCCLXXVI) was a Leap year starting on Saturday (link will display the full calendar of the Gregorian Calendar (or a Leap year

Ludwig Boltzmann and co-workers in Graz, 1887. (standing, from the left) Nernst, Streintz, Arrhenius, Hiecke, (sitting, from the left) Aulinger, Ettingshausen, Boltzmann, Klemenčič, Hausmanninger

In 1872, long before women were admitted to Austrian universities, he met Henriette von Aigentler, an aspiring teacher of mathematics and physics in Graz. Walther Hermann Nernst ( June 25, 1864 &ndash November 18, 1941) was a German Physicist who is known for his theories Svante August Arrhenius ( February 19, 1859 &ndash October 2, 1927) was a Swedish Scientist, originally a Physicist Ignacij Klemenčič ( February 6, 1853 - September 5, 1901) was a Slovene Physicist. She was refused permission to unofficially audit lectures, and Boltzmann advised her to appeal; she did, successfully. On July 17, 1876 Ludwig Boltzmann married Henriette von Aigentler; they had three daughters and two sons. Events 180 - Twelve inhabitants of Scillium in North Africa are executed for being Christians Boltzmann went back to Graz to take up the chair of Experimental Physics. Among his students in Graz were Svante Arrhenius and Walther Nernst. Svante August Arrhenius ( February 19, 1859 &ndash October 2, 1927) was a Swedish Scientist, originally a Physicist Walther Hermann Nernst ( June 25, 1864 &ndash November 18, 1941) was a German Physicist who is known for his theories ^[1][2] He spent 14 happy years in Graz and it was there that he developed his statistical concept of nature. In 1885 he became a member of the Imperial Austrian Academy of Sciences and in 1887 he became the President of the University of Graz. Year 1885 ( MDCCCLXXXV) was a Common year starting on Thursday (link will display the full calendar of the Gregorian calendar (or a Common The Austrian Academy of Sciences ("Österreichische Akademie der Wissenschaften" is a legal entity under the special protection of the Federal Republic of Austria Year 1887 ( MDCCCLXXXVII) was a Common year starting on Saturday (link will display the full calendar of the Gregorian calendar (or a Common The University of Graz ( German, Karl-Franzens-Universität Graz) a University located in Graz, Austria, is the second-largest

Boltzmann was appointed to the Chair of Theoretical Physics at the University of Munich in Bavaria, Germany in 1890. The Ludwig Maximilian University of Munich (Ludwig-Maximilians-Universität München also known as LMU, is a University in Munich and with more Bavaria ( German:, with an area of 70553 Km² (27241 square miles and almost 12 Year 1890 ( MDCCCXC) was a Common year starting on Wednesday (link will display the full calendar of the Gregorian calendar (or a Common In 1893, Boltzmann succeeded his teacher Joseph Stefan as Professor of Theoretical Physics at the University of Vienna.

Final years

However, Boltzmann did not get along with some of his colleagues in Vienna, particularly Ernst Mach, who became a professor of philosophy and history of sciences in 1895. Ernst Mach (max ( February 18, 1838 &ndash February 19, 1916) was an Austrian Physicist and Philosopher and Thus in 1900 Boltzmann went to the University of Leipzig, on the invitation of Wilhelm Ostwald. Year 1900 ( MCM) was an exceptional Common year starting on Monday (link will display the full calendar of the Gregorian calendar The University of Leipzig (Universität Leipzig located in Leipzig in the Free State of Saxony, Germany, is one of the oldest universities Friedrich Wilhelm Ostwald ( Latvian: Vilhelms Ostvalds; September 2, 1853 &ndash April 4, 1932) was a Baltic After the retirement of Mach due to bad health, Boltzmann came back to Vienna in 1902. Year 1902 ( MCMII) was a Common year starting on Wednesday (link will display calendar of the Gregorian calendar (or a Common year starting His students included Karl Przibram, Paul Ehrenfest and Lise Meitner. “ Karl Pribram ” may refer to Karl Přibram ( 22 December 1877 – 15 July 1973) Austrian-born economist Paul Ehrenfest ( January 18, 1880 – September 25, 1933) was an Austrian Physicist and Mathematician, who Lise Meitner (7 or 17 November 1878 &ndash 27 October 1968 was an Austrian born later Swedish physicist who studied Radioactivity and

In Vienna, Boltzmann not only taught physics but also lectured on philosophy. Boltzmann’s lectures on natural philosophy were very popular, and received a considerable attention at that time. His first lecture was an enormous success. Even though the largest lecture hall had been chosen for it, the people stood all the way down the staircase. Because of the great successes of Boltzmann’s philosophical lectures, the Emperor invited him for a reception at the Palace.

Boltzmann was subject to rapid alternation of depressed moods with elevated, expansive or irritable moods, likely the symptoms of undiagnosed Bipolar Disorder. He himself jestingly attributed his rapid swings in temperament to the fact that he was born during the night between Mardi Gras and Ash Wednesday. " Mardi Gras " ( French for Fat Tuesday) is the day before Ash Wednesday. In the Western Christian Calendar, Ash Wednesday is the first day of Lent and occurs forty days before Easter (excluding Sundays Meitner relates that those who were close to Boltzmann were aware of his bouts of severe depression and his suicide attempts.

On September 5, 1906, while on a summer vacation in Duino, near Trieste, Boltzmann hanged himself during an attack of depression. Events 1590 - Alexander Farnese 's army forces Henry IV of France to raise the siege of Paris. Year 1906 ( MCMVI) was a Common year starting on Monday (link will display full calendar of the Gregorian calendar (or a Common year starting Duino ( Devin in Slovenian, Tybein in German) is a town in the coastal part of the municipality ( Comune) of Duino-Aurisina Trieste (Trieste Slovene and Croatian: Trst; German: Triest) is a city and port in northeastern Italy very near to A mood disorder is the term given for a group of diagnoses in the DSM IV TR classification system where a disturbance in the person's emotional mood is hypothesised He is buried in the Viennese Zentralfriedhof and his tombstone reads S=k. The Zentralfriedhof (Central Cemetery is situated in the district of Simmering, Simmeringer Hauptstraße 230–244 Vienna 1110 Austria, and is the  log W.

Physics

Boltzmann's most important scientific contributions were in kinetic theory, including the Maxwell-Boltzmann distribution for molecular speeds in a gas. Kinetic theory (or kinetic theory of gases) attempts to explain Macroscopic properties of Gases such as pressure temperature or volume by considering The Maxwell–Boltzmann distribution is a Probability distribution with applications in Physics and Chemistry. In addition, Maxwell-Boltzmann statistics and the Boltzmann distribution over energies remain the foundations of classical statistical mechanics. In Statistical mechanics, Maxwell–Boltzmann statistics describes the statistical distribution of material particles over various energy states in Thermal equilibrium WikipediaWikiProject Probability#Standards for a discussion of standards used for probability distribution articles such as this one Classical mechanics is used for describing the motion of Macroscopic objects from Projectiles to parts of Machinery, as well as Astronomical objects They are applicable to the many phenomena that do not require quantum statistics and provide a remarkable insight into the meaning of temperature. A phenomenon (from Greek φαινόμενoν, pl φαινόμενα - phenomena) is any observable occurrence In Statistical mechanics, Maxwell–Boltzmann statistics describes the statistical distribution of material particles over various energy states in Thermal equilibrium Thermodynamic temperature is the absolute measure of Temperature and is one of the principal parameters of Thermodynamics.

Boltzmann’s 1898 I₂ molecule diagram showing atomic “sensitive region” (α, β) overlap.

Much of the physics establishment did not share his belief in the reality of atoms and molecules — a belief shared, however, by Maxwell in Scotland and Gibbs in the United States; and by most chemists since the discoveries of John Dalton in 1808. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. History See also Atomic theory, Atomism The concept that matter is composed of discrete units and cannot be divided into arbitrarily tiny In Chemistry, a molecule is defined as a sufficiently stable electrically neutral group of at least two Atoms in a definite arrangement held together by James Clerk Maxwell (13 June 1831 &ndash 5 November 1879 was a Scottish mathematician and theoretical physicist. Scotland ( Gaelic: Alba) is a Country in northwest Europethat occupies the northern third of the island of Great Britain. Josiah Willard Gibbs ( February 11, 1839 &ndash April 28, 1903) was an American theoretical Physicist, Chemist The United States of America —commonly referred to as the The history of Chemistry begins with the discovery of Fire, then Metallurgy which allowed purification of metals and the making of alloys as well as the exploitation Chemistry (from Egyptian kēme (chem meaning "earth") is the Science concerned with the composition structure and properties John Dalton FRS (6 September 1766 &ndash 27 July 1844 was an English Chemist, Meteorologist and Physicist. He had a long-running dispute with the editor of the preeminent German physics journal of his day, who refused to let Boltzmann refer to atoms and molecules as anything other than convenient theoretical constructs. Germany, officially the Federal Republic of Germany ( ˈbʊndəsʁepuˌbliːk ˈdɔʏtʃlant is a Country in Central Europe. The word theory has many distinct meanings in different fields of Knowledge, depending on their methodologies and the context of discussion. Only a couple of years after Boltzmann's death, Perrin's studies of colloidal suspensions (1908-1909) confirmed the values of Avogadro's number and Boltzmann's constant, and convinced the world that the tiny particles really exist. Jean Baptiste Perrin ( September 30, 1870 &ndash April 17, 1942) was a French Physicist and Nobel laureate. A colloid is a type of mechanical Mixture where one substance is dispersed evenly throughout another The Avogadro constant (symbols L, N A also called Avogadro's number, is the number of "elementary entities" (usually Atoms Bridge from macroscopic to microscopic physics Boltzmann's constant k is a bridge between Macroscopic and microscopic physics This article focuses on the historical models of the atom For a history of the study of how atoms combine to form molecules see History of the molecule.

To quote Planck, "The logarithmic connection between entropy and probability was first stated by L. 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 Thermodynamics (a branch of Physics) entropy, symbolized by S, is a measure of the unavailability of a system ’s Energy Probability is the likelihood or chance that something is the case or will happen Boltzmann in his kinetic theory of gases"^[3]This famous formula for entropy S is^{[4] [5]}

where k = 1. Kinetic theory (or kinetic theory of gases) attempts to explain Macroscopic properties of Gases such as pressure temperature or volume by considering 3806505(24) × 10⁻²³ J K⁻¹ is Boltzmann's constant, and the logarithm is taken to the natural base e. 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 Bridge from macroscopic to microscopic physics Boltzmann's constant k is a bridge between Macroscopic and microscopic physics 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 W is the Wahrscheinlichkeit, the frequency of occurrence of a macrostate^[6] or, more precisely, the number of possible microstates corresponding to the macroscopic state of a system — number of (unobservable) "ways" the (observable) thermodynamic state of a system can be realized by assigning different positions and momenta to the various molecules. In Statistics the frequency of an event i is the number ni of times the event occurred in the Experiment or the study 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 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 In Physics, thermodynamics (from the Greek θερμη therme meaning " Heat " and δυναμις dynamis meaning " In Mathematics and its applications a coordinate system is a system for assigning an n - Tuple of Numbers or scalars to each point In Classical mechanics, momentum ( pl momenta SI unit kg · m/s, or equivalently N · s) is the product Boltzmann’s paradigm was an ideal gas of N identical particles, of which N_i are in the i-th microscopic condition (range) of position and momentum. The word paradigm ( Greek:παράδειγμα (paradigmacomposite from para- and the verb δείχνυμι "to show" as a whole -roughly- meaning "example" 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 W can be counted using the formula for permutations

where i ranges over all possible molecular conditions. In Statistical mechanics, Maxwell–Boltzmann statistics describes the statistical distribution of material particles over various energy states in Thermal equilibrium (! denotes factorial. Definition The factorial function is formally defined by n!=\prod_{k=1}^n k ) The "correction" in the denominator is because identical particles in the same condition are indistinguishable. Identical particles, or indistinguishable particles, are particles that cannot be distinguished from one another even in principle W is called the "thermodynamic probability" since it is an integer greater than one, while mathematical probabilities are always numbers between zero and one. The integers (from the Latin integer, literally "untouched" hence "whole" the word entire comes from the same origin but via French Probability theory is the branch of Mathematics concerned with analysis of random phenomena A number is an Abstract object, tokens of which are Symbols used in Counting and measuring.

The equation for S is engraved on Boltzmann's tombstone at the Vienna Zentralfriedhof — his second grave. A headstone, tombstone or gravestone is a marker normally carved from stone, placed over or next to the site of a Burial The Zentralfriedhof (Central Cemetery is situated in the district of Simmering, Simmeringer Hauptstraße 230–244 Vienna 1110 Austria, and is the

The Boltzmann equation

Boltzmann's bust in the courtyard arcade of the main building, University of Vienna. The University of Vienna (Universität Wien is a Public university located in Vienna, Austria.

Main article: Boltzmann equation

The Boltzmann equation was developed to describe the dynamics of an ideal gas. The Boltzmann equation, also often known as the Boltzmann transport equation, devised by Ludwig Boltzmann, describes the statistical distribution of 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

where f represents the distribution function of single-particle position and momentum at a given time (see the Maxwell-Boltzmann distribution), F is a force, m is the mass of a particle, t is the time and v is an average velocity of particles. The Maxwell–Boltzmann distribution is a Probability distribution with applications in Physics and Chemistry.

This equation describes the temporal and spatial variation of the probability distribution for the position and momentum of a density distribution of a cloud of points in single-particle phase space. For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of Space is the extent within which Matter is physically extended and objects and Events have positions relative to one another In Mathematics and Physics, a phase space, introduced by Willard Gibbs in 1901 is a Space in which all possible states of a System (See Hamiltonian mechanics. Hamiltonian mechanics is a re-formulation of Classical mechanics that was introduced in 1833 by Irish mathematician William Rowan Hamilton. ) The first term on the left-hand side represents the explicit time variation of the distribution function, while the second term gives the spatial variation, and the third term describes the effect of any force acting on the particles. The right-hand side of the equation represents the effect of collisions.

Boltzmann's grave in the Zentralfriedhof, Vienna, with bust and entropy formula. The Zentralfriedhof (Central Cemetery is situated in the district of Simmering, Simmeringer Hauptstraße 230–244 Vienna 1110 Austria, and is the

In principle, the above equation completely describes the dynamics of an ensemble of gas particles, given appropriate boundary conditions. In Mathematics, in the field of Differential equations a boundary value problem is a Differential equation together with a set of additional restraints This first-order differential equation has a deceptively simple appearance, since f can represent an arbitrary single-particle distribution function. A differential equation is a mathematical Equation for an unknown function of one or several variables that relates the values of the Also, the force acting on the particles depends directly on the velocity distribution function f. In Physics, a force is whatever can cause an object with Mass to Accelerate. The Boltzmann equation is notoriously difficult to integrate. The European Space Agency 's INTErnational Gamma-Ray Astrophysics Laboratory ( INTEGRAL) is detecting some of the most energetic radiation that comes from space David Hilbert spent years trying to solve it without any real success. David Hilbert ( January 23, 1862 &ndash February 14, 1943) was a German Mathematician, recognized as one of the most

The form of the collision term assumed by Boltzmann was approximate. However for an ideal gas the standard Chapman-Enskog solution of the Boltzmann equation is highly accurate. 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 It is expected to lead to incorrect results for an ideal gas only under shock wave conditions. 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 For the music album by Converter see Shock Front For the 1977 horror film see Shock Waves A shock wave (also called

Boltzmann tried for many years to "prove" the second law of thermodynamics using his gas-dynamical equation — his famous H-theorem. 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 H-theorem, introduced by Boltzmann in 1872, describes the increase in the Entropy of an Ideal gas in an irreversible However the key assumption he made in formulating the collision term was "molecular chaos", an assumption which breaks time-reversal symmetry as is necessary for anything which could imply the second law. In Kinetic theory in Physics, molecular chaos is the assumption that the velocities of colliding particles are uncorrelated and independent of position CPT symmetry is a fundamental symmetry of Physical laws under transformations that involve the inversions of charge, parity and It was from the probabilistic assumption alone that Boltzmann's apparent success emanated, so his long dispute with Loschmidt and others over Loschmidt's paradox ultimately ended in his failure. Jan or Johann Josef Loschmidt ( March 15 1821 - July 8 1895) who referred to himself mostly as 'Josef' (omitting his first name Loschmidt's paradox, also known as the reversibility paradox, is the objection that it should not be possible to deduce an irreversible process from time-symmetric dynamics

Finally, in the 1970s E. G. D. Cohen and J. R. Dorfman proved that a systematic (power series) extension of the Boltzmann equation to high densities is mathematically impossible. Consequently nonequilibrium statistical mechanics for dense gases and liquids focuses on the Green-Kubo relations, the fluctuation theorem, and other approaches instead. Non-equilibrium thermodynamics is a branch of Thermodynamics concerned with studying Time -dependent Thermodynamic systems irreversible transformations This page is about the physical properties of gas as a state of matter Liquid is one of the principal States of matter. A liquid is a Fluid that has the particles loose and can freely form a distinct surface at the boundaries of Green–Kubo relations give exact mathematical expression for transport coefficients in terms of integrals of time correlation functions The fluctuation theorem (FT is a theorem from Statistical mechanics dealing with the relative probability that the Entropy of a system which is currently away from

Energetics of evolution

Boltzmann's views played an essential role in the development of energetics, the scientific study of energy flows under transformation. Energetics is the scientific study of energy flows and storages under transformation In 1922, for example, Alfred J. Lotka referred to Boltzmann as one of the first proponents of the proposition that available energy, also called exergy, can be understood as the fundamental object under contention in the biological, or life-struggle and therefore also in the evolution of the organic world. Alfred James Lotka ( March 2, 1880 - December 5, 1949) was a US Mathematician, Physical chemist, and Statistician "Available energy" redirects here For the meaning of the term in particle collisions see Available energy (particle collision. ^[7] Lotka interpreted Boltzmann's view to imply that available energy could be the central concept that unified physics and biology as a quantitative physical principle of evolution. In the forward to Boltzmann's Theoretical Physics and Philosophical Problems, S. R. de Groot noted that

Howard T. Odum later sought to develop these views when looking at the evolution of ecological systems, and suggested that the maximum power principle was an example of Darwin's law of natural selection. Howard Thomas Odum (1924 Chapel Hill North Carolina &ndash2002 Gainesville Florida) (also known as Tom or just H The maximum power principle has been proposed as the fourth principle of energetics in open system Thermodynamics, where an example of an open system Natural selection is the process by which favorable Heritable traits become more common in successive Generations of a Population of

Significant contributions

1872 - Boltzmann equation; H-theorem

1877 - Boltzmann distribution; relationship between thermodynamic entropy and probability. Year 1872 ( MDCCCLXXII) was a Leap year starting on Monday (link will display the full calendar of the Gregorian Calendar (or a Leap year The Boltzmann equation, also often known as the Boltzmann transport equation, devised by Ludwig Boltzmann, describes the statistical distribution of In Thermodynamics, the H-theorem, introduced by Boltzmann in 1872, describes the increase in the Entropy of an Ideal gas in an irreversible Year 1877 ( MDCCCLXXVII) was a Common year starting on Monday (link will display the full calendar of the Gregorian calendar (or a Common WikipediaWikiProject Probability#Standards for a discussion of standards used for probability distribution articles such as this one

1884 - Derivation of the Stefan-Boltzmann law

Evaluations

Closely associated with a particular interpretation of the second law of thermodynamics, he is also credited in some quarters with anticipating quantum mechanics. Year 1884 ( MDCCCLXXXIV) was a Leap year starting on Tuesday (link will display the full calendar of the Gregorian calendar (or a Leap year The Stefan–Boltzmann law, also known as Stefan's law, states that the total Energy radiated per unit surface Area of a Black body in unit The second law of Thermodynamics is an expression of the universal law of increasing Entropy, stating that the entropy of an Isolated system which Quantum mechanics is the study of mechanical systems whose dimensions are close to the Atomic scale such as Molecules Atoms Electrons

For detailed and technically informed account of Boltzmann's contributions to statistical mechanics consult the article by E. G. D. Cohen.

See also

• Boltzmann brain
• The Boltzmann machine
• History of the molecule
• List of Austrian scientists
• List of Austrians
• Lattice Boltzmann methods, a new method in Computational fluid dynamics which utilizes the theories of Boltzmann. A Boltzmann brain is a hypothesized self-aware entity which arises due to random fluctuations out of a state of chaos A Boltzmann machine is the name given to a type of stochastic recurrent neural network by Geoffrey Hinton and Terry Sejnowski. In Chemistry, the history of the Molecule traces the origins of the concept or idea of the existence of strong chemical bonds between two or more Atoms This is a list of Austrian scientists and scientists from the Austria of Austria-Hungary. The following list is a selection of famous Austrians. For full lists of all famous Austrians please view the sublists Lattice Boltzmann methods (LBM is a class of Computational fluid dynamics (CFD methods for fluid simulation Computational fluid dynamics (CFD is one of the branches of Fluid mechanics that uses Numerical methods and algorithms to solve and analyze problems that involve
• Philosophy of thermal and statistical physics

References

Further reading

• Brush, Stephen G. The maximum power principle has been proposed as the fourth principle of energetics in open system Thermodynamics, where an example of an open system (ed. & tr. ), Boltzmann, Lectures on Gas Theory, Berkeley, CA: U. of California Press, 1964
• Brush, Stephen G. (ed. ), Kinetic Theory, New York: Pergamon Press, 1965
• Brush, Stephen G. (1970). "Boltzmann", in Charles Coulston Gillispie (ed. ): Dictionary of Scientific Biography. New York: Scribner. ISBN 0-684-16962-2.  
• Brush, Stephen G. (1986). The Kind of Motion We Call Heat: A History of the Kinetic Theory of Gases. Amsterdam: North-Holland. ISBN 0-7204-0370-7.  
• P. Ehrenfest & T. Ehrenfest (1911) Begriffliche Grundlagen der statistischen Auffassung in der Mechanik, in: Encyklopädie der mathematischen Wissenschaften mit Einschluß ihrer Anwendungen. Paul Ehrenfest ( January 18, 1880 – September 25, 1933) was an Austrian Physicist and Mathematician, who Tatyana Alexeyevna Afanasyeva (Татьяна Алексеевна Афанасьева ( Kiev, November 19, 1876 &ndash Leiden, April Band IV, 2. Teil ( F. Klein and C. Müller (eds. ). Leipzig: Teubner, pp. 3–90. Translated as The conceptual Foundations of the Statistical Approach in Mechanics. New York: Cornell University Press, 1959. ISBN 0-486-49504-3
• Brush, Stephen G. (1970). "Boltzmann", in Charles Coulston Gillispie (ed. ): Dictionary of Scientific Biography. New York: Scribner. ISBN 0-684-16962-2.  
• Fasol-Boltzmann, Ilse Maria; Gerhard Fasol (1996). Ludwig Boltzmann (1844-1906) Zum hundertsten Todestag. Wien New York: Springer Verlag. ISBN 3-211-33140-9.  
• Planck, Max (1914). The Theory of Heat Radiation. P. Blakiston Son & Co.   English translation by Morton Masius of the 2nd ed. of Waermestrahlung. Reprinted by Dover (1959) & (1991). ISBN 0-486-66811-8
• Everdell, William R (1988). "The Problem of Continuity and the Origins of Modernism: 1870-1913". History of European Ideas 9 (5): 531-552. doi:10.1016/0191-6599(88)90001-0. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document. ISSN 0191-6599. An International Standard Serial Number ( ISSN) is a unique eight-digit number used to identify a print or electronic Periodical publication.  
• Klein, Martin J. (1973). "The Development of Boltzmann’s Statistical Ideas", in E. G. D. Cohen and W. Thirring (eds): The Boltzmann Equation: Theory and Applications, Acta physica Austriaca Suppl. 10. Wien: Springer, 53–106. ISBN 0-387-81137-0.  
• Tolman, Richard C. (1938). The Principles of Statistical Mechanics. Oxford University Press.   Reprinted: Dover (1979). ISBN 0-486-63896-0
• Gibbs, J. Willard (1901). Josiah Willard Gibbs ( February 11, 1839 &ndash April 28, 1903) was an American theoretical Physicist, Chemist Elementary Principles in Statistical Mechanics. Ox Bow Press (1981). ISBN 0-918024-19-6.  
• Lindley, David (2001). David Lindley (born 1956 is a theoretical physicist and author Boltzmann's Atom: The Great Debate That Launched A Revolution In Physics. ISBN 0-684-85186-5.  
• Lotka, A. J. (1922). "Contribution to the energetics of evolution" (PDF fulltext). Proc Nat Acad Sci USA 8 (6): 147. doi:10.1073/pnas.8.6.147. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document. ISSN 0027-8424. An International Standard Serial Number ( ISSN) is a unique eight-digit number used to identify a print or electronic Periodical publication.  

External links

• Ruth Lewin Sime, Lise Meitner: A Life in Physics Chapter One: Girlhood in Vienna gives Lise Meitner's account of Boltzmann's life and career.
• Ludwig Boltzmann, Universität Wien.
• Ali Eftekhari, Ludwig Boltzmann (1844–1906)
• O'Connor, John J. & Robertson, Edmund F. , “Ludwig Boltzmann”, MacTutor History of Mathematics archive 
• Scienceworld biography
• Uffink, Jos (2004). The MacTutor History of Mathematics archive is an award-winning website maintained by John J Boltzmann's Work in Statistical Physics. Retrieved on 2007-06-11. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 1184 BC - Trojan War: Troy is sacked and burned according to the calculations of Eratosthenes. Article first published in the Stanford Encyclopedia of Philosophy
• Shannon, Claude E. (1948). The Mathematical Theory of Communication. Retrieved on 2007-06-11. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 1184 BC - Trojan War: Troy is sacked and burned according to the calculations of Eratosthenes.
• Ludwig Boltzmann's Gravesite
• Rajasekar, S. ; Athavan, N. (2006-09-07). Year 2006 ( MMVI) was a Common year starting on Sunday of the Gregorian calendar. Events 1251 BC - A Solar eclipse on this date might mark the birth of legendary Heracles at Thebes Greece. Ludwig Edward Boltzmann. Retrieved on 2007-05-31. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 1279 BC - Rameses II (The Great (19th dynasty becomes pharaoh of Ancient Egypt.