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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. This puts the time reversal symmetry of (almost) all known low-level fundamental physical processes at odds with any attempt to infer from them the second law of thermodynamics which describes the behaviour of macroscopic systems. T Symmetry is the symmetry of physical laws under a Time reversal transformation &mdash T t \mapsto -t The second law of Thermodynamics is an expression of the universal law of increasing Entropy, stating that the entropy of an Isolated system which Both of these are well-accepted principles in physics, with sound observational and theoretical support, yet they seem to be in conflict; hence the paradox. A paradox is a true statement or group of statements that leads to a Contradiction or a situation which defies intuition; or inversely

Johann Loschmidt's criticism was provoked by the H-theorem of Boltzmann, which was an attempt to explain using kinetic theory the increase of entropy in an ideal gas from a non-equilibrium state, when the molecules of the gas are allowed to collide. Jan or Johann Josef Loschmidt ( March 15 1821 - July 8 1895) who referred to himself mostly as 'Josef' (omitting his first name In Thermodynamics, the H-theorem, introduced by Boltzmann in 1872, describes the increase in the Entropy of an Ideal gas in an irreversible Ludwig Eduard Boltzmann ( February 20, 1844 &ndash September 5, 1906) was an Austrian Physicist famous for his founding Kinetic theory (or kinetic theory of gases) attempts to explain Macroscopic properties of Gases such as pressure temperature or volume by considering Loschmidt pointed out in 1876 that if there is a motion of a system from time t0 to time t1 to time t2 that leads to a steady decrease of H (increase of entropy) with time, then there is another allowed state of motion of the system at t1, found by reversing all the velocities, in which H must increase. Year 1876 ( MDCCCLXXVI) was a Leap year starting on Saturday (link will display the full calendar of the Gregorian Calendar (or a Leap year In Thermodynamics (a branch of Physics) entropy, symbolized by S, is a measure of the unavailability of a system ’s Energy This revealed that one of the key assumptions in Boltzmann's theorem was flawed, namely that of molecular chaos, that all the particle velocities were completely uncorrelated. In Kinetic theory in Physics, molecular chaos is the assumption that the velocities of colliding particles are uncorrelated and independent of position One can assert that the correlations are uninteresting, and therefore decide to ignore them; but if one does so, one has changed the conceptual system, injecting an element of time-asymmetry by that very action.

Reversible laws of motion cannot explain why we experience our world to be in such a comparatively low state of entropy at the moment (compared to the equilibrium entropy of universal heat death); and to have been at even lower entropy in the past. 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

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Arrow of time

Any process that happens regularly in the forward direction of time but rarely or never in the opposite direction, such as entropy increasing in an isolated system, defines what physicists call an arrow of time in nature. This term only refers to an observation of an asymmetry in time, it is not meant to suggest an explanation for such asymmetries. Loschmidt's paradox is equivalent to the question of how it is possible that there could be a thermodynamic arrow of time given time-symmetric fundamental laws, since time-symmetry implies that for any process compatible with these fundamental laws, a reversed version that looked exactly like a film of the first process played backwards would be equally compatible with the same fundamental laws, and would even be equally probable if one were to pick the system's initial state randomly from the phase space of all possible states for that system. Entropy is the only quantity in the physical sciences that "picks" a particular direction for time sometimes called an Arrow of time. In Mathematics and Physics, a phase space, introduced by Willard Gibbs in 1901 is a Space in which all possible states of a System

Although most of the arrows of time described by physicists are thought to be special cases of the thermodynamic arrow, there are a few that are believed to be unconnected, like the cosmological arrow of time based on the fact that the universe is expanding rather than contracting, and the fact that there are a few processes in particle physics actually violate time-symmetry, although they respect a related symmetry known as CPT symmetry. CPT symmetry is a fundamental symmetry of Physical laws under transformations that involve the inversions of charge, parity and In the case of the cosmological arrow, most physicists believe that entropy would continue to increase even if the universe began to contract (although the physicist Thomas Gold once proposed a model in which the thermodynamic arrow would reverse in this phase). Thomas Gold ( May 22, 1920 &ndash June 22, 2004) was an Austrian born Astrophysicist, a professor of Astronomy In the case of the violations of time-symmetry in particle physics, the situations in which they occur are rare and are only known to involve a few types of meson particles. In Particle physics, a meson is a strongly interacting Boson &mdashthat is a Hadron with integer spin. Furthermore, due to CPT symmetry reversal of time direction is equivalent to renaming particles as antiparticles and vice versa. CPT symmetry is a fundamental symmetry of Physical laws under transformations that involve the inversions of charge, parity and to most kinds of particles, there is an associated antiparticle with the same Mass and opposite Electric charge. Therefore this cannot explain Loschmidt's paradox.

Fluctuation theorem

One approach to handling Loschmidt's paradox is the fluctuation theorem, proved by Denis Evans and Debra Searles, which gives a numerical estimate of the probability that a system away from equilibrium will have a certain change in entropy over a certain amount of time. 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 Denis James Evans, (born April 19, 1951 in Sydney Australia is a Professor in the Research School of Chemistry at the Australian National University Debra Searles is the professional name for an Australian theoretical chemist whose married name is Debra Bernhardt The theorem is proved with the exact time reversible dynamical equations of motion and the Axiom of Causality. The Axiom of Causality is the proposition that everything in the universe has a cause and is thus an effect of that cause The fluctuation theorem is proved utilizing the fact that dynamics is time reversible. Quantitative predictions of this theorem have been confirmed in laboratory experiments at the Australian National University conducted by Edith M. Sevick et al. using optical tweezers apparatus. An optical tweezer is a scientific instrument that uses a focused Laser beam to provide an attractive or repulsive force (typically on the order of pico Newtons) depending

However, the fluctuation theorem assumes that the system is initially in a non-equilibrium state, so it can be argued that the theorem only verifies the time-asymmetry of the second law of thermodynamics based on an a priori assumption of time-asymmetric boundary conditions. If no low-entropy boundary conditions in the past are assumed, the fluctuation theorem should give exactly the same predictions in the reverse time direction as it does in the forward direction, meaning that if you observe a system in a nonequilibrium state, you should predict that its entropy was more likely to have been higher at earlier times as well as later times. This prediction would be at odds with everyday experience, since if you film a typical nonequilibrium system and play the film in reverse, you typically see the entropy steadily decreasing rather than increasing. Thus we still have no explanation for the arrow of time that is defined by the observation that the fluctuation theorem gives correct predictions in the forward direction but not the backward direction, so the fundamental paradox remains unsolved.

Note, however, that if you were looking at an isolated system which had reached equilibrium long in the past, so that any departures from equilibrium were the result of random fluctuations, then the backwards prediction would be just as accurate as the forward one, because if you happen to see the system in a nonequilibrium state it is overwhelmingly likely that you are looking at the minimum-entropy point of the random fluctuation (if it were truly random, there's no reason to expect it to continue to drop to even lower values of entropy, or to expect it had dropped to even lower levels earlier), meaning that entropy was probably higher in both the past and the future of that state. So, the fact that the time-reversed version of the fluctuation theorem does not ordinarily give accurate predictions in the real world is reason to think that the nonequilibrium state of the universe at the present moment is not simply a result of a random fluctuation, and that there must be some other explanation such as the Big Bang starting the universe off in a low-entropy state (see below). The Big Bang is the cosmological model of the Universe that is best supported by all lines of scientific evidence and Observation.

The Big Bang

Another way of dealing with Loschmidt's paradox is to see the second law as an expression of a set of boundary conditions, in which our universe's time coordinate has a low-entropy endpoint: the Big Bang. The Big Bang is the cosmological model of the Universe that is best supported by all lines of scientific evidence and Observation. From this point of view, the arrow of time is determined entirely by the direction that leads to the Big Bang, and a hypothetical universe with a maximum-entropy Big Bang would have no arrow of time. The theory of cosmic inflation tries to give reason why the early universe had such a low entropy. In Physical cosmology, cosmic inflation is the idea that the nascent Universe passed through a phase of exponential expansion that

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