Nonequilibrium Thermodynamics of Time-dependent Langevin Systems: Energy Balance Relation and the Extended Form of the Second Law

TL;DR

This paper develops a comprehensive nonequilibrium thermodynamic framework for time-dependent Langevin systems, deriving energy balance relations and an extended second law applicable to transient processes, with practical examples.

Contribution

It introduces a unified energy balance relation and an explicit mathematical form of the extended second law for time-dependent Langevin dynamics.

Findings

Derived a general energy balance equality for nonequilibrium Langevin systems.

Proposed an explicit mathematical interpretation of the extended second law.

Applied the theory to classical thermodynamic processes.

Abstract

A general nonequilibrium thermodynamic theory is developed for time-dependent Langevin dynamics, starting from the common definition of nonequilibrium Gibbs entropy. It is shown that the notations appearing in the First and the Second Law of thermodynamics could be consistently applied to transient nonequilibrium processes. We find out a general equality representing the energy balance relation for the system, and further an explicit mathematical interpretation for the extended form of the Second Law is proposed, which only comes into existence in the time-dependent case. More applications to several classic thermodynamic processes are finally included.