Universal Ideal Behavior and Macroscopic Work Relation of Linear Irreversible Stochastic Thermodynamics

TL;DR

This paper explores the fundamental stochastic thermodynamics of linear irreversible systems modeled by Ornstein-Uhlenbeck processes, revealing universal thermodynamic behavior and deriving a macroscopic work relation that connects microscopic fluctuations with thermodynamic laws.

Contribution

It establishes a theoretical framework linking Ornstein-Uhlenbeck processes to thermodynamics via the Helmholtz theorem, introducing a universal ideal behavior and a macroscopic work relation.

Findings

Universal ideal thermodynamic behavior in linear irreversible systems.

Derivation of a macroscopic non-equilibrium work relation.

Connection between microscopic fluctuations and thermodynamic laws.

Abstract

We revisit the Ornstein-Uhlenbeck (OU) process as the fundamental mathematical description of linear irreversible phenomena, with fluctuations, near an equilibrium. By identifying the underlying circulating dynamics in a stationary process as the natural generalization of classical conservative mechanics, a bridge between a family of OU processes with equilibrium fluctuations and thermodynamics is established through the celebrated Helmholtz theorem. The Helmholtz theorem provides an emergent macroscopic "equation of state" of the entire system, which exhibits a universal ideal thermodynamic behavior. Fluctuating macroscopic quantities are studied from the stochastic thermodynamic point of view and a non-equilibrium work relation is obtained in the macroscopic picture, which may facilitate experimental study and application of the equalities due to Jarzynski, Crooks, and Hatano and Sasa.