Linear Stochastic Thermodynamics

TL;DR

This paper develops a unified linear stochastic thermodynamics framework for open systems near equilibrium, incorporating nonconservative forces, time-dependent driving, and entropy production decomposition, extending classical thermodynamics principles.

Contribution

It introduces a generalized Onsager theory and a novel entropy production decomposition for arbitrary periodic drivings, advancing the understanding of near-equilibrium thermodynamics with nonconservative forces.

Findings

Derived a symmetric generalized Onsager matrix.

Expressed entropy production as a sum over driving frequencies.

Proved a minimum entropy production principle near equilibrium.

Abstract

We study the thermodynamics of open systems weakly driven out-of-equilibrium by nonconservative and time-dependent forces using the linear regime of stochastic thermodynamics. We make use of conservation laws to identify the potential and nonconservative components of the forces. This allows us to formulate a unified near-equilibrium thermodynamics. For nonequilibrium steady states, we obtain an Onsager theory ensuring nonsingular response matrices that is consistent with phenomenological linear irreversible thermodynamics. For time-dependent driving protocols that do not produce nonconservative forces, we identify the equilibrium ensemble from which Green-Kubo relations are recovered. For arbitrary periodic drivings, the averaged entropy production (EP) is expressed as an independent sum over each driving frequency of non-negative contributions. These contributions are bilinear in the nonconservative and conservative forces and involve a novel generalized Onsager matrix that is symmetric. In the most general case of arbitrary time-dependent drivings, we advance a novel decomposition of the EP rate into two non-negative contributions - one solely due to nonconservative forces and the other solely due to deviation from the instantaneous steady-state - directly implying a minimum entropy production principle close to equilibrium. This setting reveals the geometric structure of near-equilibrium thermodynamics and generalizes previous approaches to cases with nonconservative forces.