Summary
The fluctuation theorem is of fundamental importance to nonequilibrium statistical mechanics. The FT (together with the Axiom of Causality) gives a generalisation of the second law of thermodynamics which includes as a special case, the conventional second law. It is then easy to prove the Second Law Inequality and the NonEquilibrium Partition Identity. When combined with the central limit theorem, the FT also implies the famous Green-Kubo relations for linear transport coefficients, close to equilibrium. The FT is however, more general than the Green-Kubo Relations because unlike them, the FT applies to fluctuations far from equilibrium. In spite of this fact, scientists have not yet been able to derive the equations for nonlinear response theory from the FT.
The FT does not imply or require that the distribution of time averaged dissipation be Gaussian. There are many examples known where the distribution of time averaged dissipation is non-Gaussian and yet the FT (of course) still correctly describes the probability ratios.
Lastly the theoretical constructs used to prove the FT can be applied to nonequilibrium transitions between two different equilibrium states. When this is done the so-called Jarzynski equality or nonequilibrium work relation, can be derived. This equality shows how equilibrium free energy differences can be computed or measured (in the laboratory), from nonequilibrium path integrals. Previously quasi-static (equilibrium) paths were required.
The reason why the fluctuation theorem is so fundamental is that its proof requires so little. It requires:
- knowledge of the mathematical form of the initial distribution of molecular states,
- that all time evolved final states at time t, must be present with nonzero probability in the distribution of initial states (t = 0) - the so-called condition of ergodic consistency and,
- an assumption of time reversal symmetry.
In regard to the latter "assumption", all the equations of motion for either classical or quantum dynamics are in fact time reversible.
For an alternative view on the same subject see http://www.scholarpedia.org/article/Fluctuation_theorem
Read more about this topic: Fluctuation Theorem
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