Entropy and Thermodynamic second laws: New perspective - stochastic thermodynamics and fluctuation theorems

TL;DR

This paper explores the connection between entropy, the second law, and fluctuation theorems in nonequilibrium thermodynamics, emphasizing stochastic thermodynamics and the role of symmetry in entropy fluctuations.

Contribution

It introduces stochastic thermodynamics and derives various fluctuation theorems, providing a new perspective on the second law in small and nonequilibrium systems.

Findings

Derivation of fluctuation theorems for total entropy production

Explanation of the Gallavotti-Cohen symmetry in NEQ fluctuations

Quantitative predictions of entropy law violations in small systems

Abstract

Recently, there has been a considerable progress on the issue of the thermodynamic second law, which is known as the law of entropy increase or irreversibility. In particular, a novel symmetry known as the Gallavotti-Cohen symmetry is found in nonequilibrium (NEQ) fluctuations, which leads to so-called fluctuation theorems. The thermodynamic second law is a simple corollary of fluctuation theorems, from which one can predict quantitatively how often NEQ processes violate the law of entropy increase. Violations disappear in the thermodynamic limit, but can be observed reasonably well in small systems. In this article, we will briefly introduce the stochastic thermodynamics and derive various fluctuation theorems, including the total entropy production (EP), the work-free-energy relation, the excess and house-keeping EP, and the information entropy.