Derivation of a Fluctuation Theorem from the probabilistic definition of entropy

W. Pietsch

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Derivation of a Fluctuation Theorem from the probabilistic definition of entropy

W. Pietsch

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Abstract

It will be shown, how the Boltzmannian ideas on statistical physics can be naturally applied to nonequilibrium thermodynamics. A similar approach for treating nonequilibrium phenomena has been successfully used by Einstein and Smoluchowski treating fluctuations. It will be argued, that due to the reversibility of the microscopic equations, all processes - also macroscopic ones - must at least in principle be reversible. Also, a clear conceptual distinction between equilibrium and nonequilibrium states is not possible in the Boltzmannian framework, which is just the reason why these concepts should apply to nonequilibrium. In the present manuscript we derive a Fluctuation Theorem from the equation S=k ln P, where P is the probability of a state. The recently discovered Fluctuation Theorems are some of the few exact results valid far from equilibrium. Two assumptions are needed for the derivation: First, the process shall happen on certain time-scales that are large compared with the time, during which the system memorizes its initial conditions. Second, the entropy production rate averaged over all realizations of the process shall be constant during the process. We will finally point out, why a solution to the problem of macroscopic irreversibility invoking causality - as it was recently suggested in connection with the Fluctuation Theorem - cannot live up to its task.

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W. Pietsch. 2005-09-08. Derivation of a Fluctuation Theorem from the probabilistic definition of entropy. https://arxiv.org/abs/cond-mat/0509212

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