Second law of thermodynamics

The second law of thermodynamics is a law of thermodynamics that states that all work tends towards the production of greater entropy over time. Another way of saying this (known as the Clausius formulation) is that it is impossible to construct a perfect refrigerator. (This is why refrigerators always require an external power source.) An equivalent statement, known as the Kelvin-Planck formulation, is that "It is impossible for any cyclic process to occur whose sole effect is the extraction of heat from a reservoir and the perfromance of an equivalent amount of work." (If the reader is aware of the concept of heat engines, please understand that heat engines work by allowing two heat reservoirs of different temperatures to come in equilibrium with each other, and as such they do not violate the 2nd law.)

Derivation of the Second Law from Time Reversible Mechanics

The paradox of how time reversible dynamics can lead to time irreversible behaviour as summarised in the Second Law of Thermodynamics (Loschmidt's paradox) has finally been resolved with the proof of the Fluctuation theorem FT - first proposed heuristically by Evans Cohen and Morriss in 1993 and first proved by Denis Evans and Debra Searles (Evans & Searles, 1994). The Fluctuation Theorem generalises the Second Law to small systems observed for short times. It applies to all systems which obey Classical mechanics (i.e. Newtonian dynamics), regardless of density. A quantum version of the Theorem is also now known.

Related Topics:
Loschmidt's paradox - Fluctuation theorem - 1993 - Denis Evans - Classical mechanics

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The Fluctuation Theorem shows that in small systems entropy can sometimes be consumed rather than produced, but as the system size or the observation time gets longer, the probability of entropy consumption (rather than production) decreases exponentially. In the large system limit the conventional Second Law is obtained. The Evans and Searles proof of the Fluctuation Theorem is quite elementary - see Evans and Searles (2002). It uses the exact time reversible equations of motion - as embodied in the Liouville equation - and computes the probability of time averages of entropy production from a given initial distribution of molecular states.

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This use of initial (rather than final) states, is consistent with the Law of Causality which is taken as axiomatic. Causality implies that the probability of events can be computed from the probability of preceding events - that causes determine effects. It is thus seen that the Second Law of thermodynamics is a result of the Axiom of Causality. If the Universe were anti-causal (that effects determine their causes - that for example, electric currents begin to change BEFORE the applied voltage is changed!), then entropy could only decrease. In an anticausal Universe not only do currents start to flow BEFORE voltages are applied but the anti Fluctuation Theorem proves that those currents would flow AGAINST the direction of the applied voltage. The Law, or Axiom, of Causality cannot be proved. It is an often unrecognized Law of physics every bit as fundamental and unproveable as the laws of quantum or classical mechanics.

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Quantitative predictions of the Fluctuation theorem were confirmed in laboratory experiments in 2002 by Wang et al. and later by Carberry et al, . The Fluctuation Theorem has important applications in nanotechnology. These experiments confirm the predictions of the Fluctuation theorem, that as times increase, macroscopic Second Law behaviour is approached exponentially as the averaging time increases.

Related Topics:
Fluctuation theorem - Nanotechnology

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