Path-dependent Entropy Production

TL;DR

This paper rigorously derives nonequilibrium entropy production using path-integral formalism, clarifying ambiguities and connecting it to fluctuation theorems for Langevin dynamics and Brownian motion.

Contribution

It provides a rigorous quantum mechanical derivation of entropy production in nonequilibrium processes, clarifying path-dependent ambiguities.

Findings

Entropy production defined via heat reservoir changes.

Clarification of mathematical ambiguities in path-dependent entropy.

Connection to fluctuation theorems for stochastic dynamics.

Abstract

A rigorous derivation of nonequilibrium entropy production via the path-integral formalism is presented. Entropy production is defined as the entropy change piled in a heat reservoir as a result of a nonequilibrium thermodynamic process. It is a central quantity by which various forms of the fluctuation theorem are obtained. The two kinds of the stochastic dynamics are investigated: the Langevin dynamics for an even-parity state and the Brownian motion of a single particle. Mathematical ambiguities in deriving the functional form of the entropy production, which depends on path in state space, are clarified by using a rigorous quantum mechanical approach.