On microscopic entropy production, heat and fluctuation theorem

TL;DR

This paper shows that Gibbs-Shannon entropy applies to non-equilibrium systems of any size, linking microscopic entropy changes to stochastic processes and fluctuation theorems, and deriving key thermodynamic relations.

Contribution

It demonstrates the applicability of Gibbs-Shannon entropy to non-equilibrium systems and derives fluctuation theorem-based relations for heat and entropy production.

Findings

Entropy production is nonnegative on average.

Fluctuation theorem describes the variation of entropy along trajectories.

Jarzynski and Crooks relations are derived from the fluctuation theorem.

Abstract

We demonstrate that the Gibbs-Shannon entropy is applicable to non-equilibrium systems of any size and boundary conditions. The change in microscopic entropy can be attributed to the stochastic nature of dynamic processes and to the inherent uncertainties of thermodynamic systems. The latter predicts that entropy production is nonnegative on average and varies with different trajectories according to the fluctuation theorem. By contrast, heat is affiliated with stochastic processes underlying particle motions and the ensemble average over all possible trajectories leads to the Clausius inequality. The Jarzynski/Crooks equations can be readily derived by applying the fluctuation theorem to heat variation over different trajectories linking equilibrium states.