Invariance of Steady State Thermodynamics between Different Scales of Description

TL;DR

This paper demonstrates that certain thermodynamic quantities remain invariant under different scales of description in stochastic thermodynamics, supporting coarse-grained experimental approaches.

Contribution

It establishes the invariance of combined entropy-related quantities across scales, providing a theoretical foundation for steady state thermodynamics in coarse-grained systems.

Findings

Invariant sum of entropy increment and excess entropy production across scales

Justification for coarse-grained experimental thermodynamics

Validation with a mesoscopic heat engine system

Abstract

By considering general Markov stochastic dynamics and its coarse-graining, we study the framework of stochastic thermodynamics for the original and reduced descriptions corresponding to different scales. We are especially concerned with the case where the irreversible entropy production has a finite difference between the scales. We find that the sum of increment of nonequilibrium entropy and excess part of entropy production, which are key quantities in construction of steady state thermodynamics, is essentially kept invariant with respect to the change in the scales of description. This general result justifies experimental approaches toward steady state thermodynamics based on coarse-grained variables. We demonstrate our result in a mesoscopic heat engine system.