Temperature response in nonequilibrium stochastic systems

TL;DR

This paper derives a linear response theory for temperature changes in nonequilibrium stochastic systems, revealing new entropy flow contributions and introducing the concept of thermal time through a novel time rescaling method.

Contribution

It introduces a new linear response framework for nonequilibrium stochastic systems that accounts for entropy flows due to temperature imbalances and proposes a novel time rescaling approach.

Findings

Derived explicit formulas for thermal susceptibilities from correlation functions.

Identified a new form of entropy flow related to temperature unbalances.

Established a connection between time rescaling and the emergence of thermal time.

Abstract

The linear response to temperature changes is derived for systems with overdamped stochastic dynamics. Holding both in transient and steady state conditions, the results allow to compute nonequilibrium thermal susceptibilities from unperturbed correlation functions. These correlations contain a novel form of entropy flow due to temperature unbalances, next to the standard entropy flow of stochastic energetics and to complementary time-symmetric dynamical aspects. Our derivation hinges on a time rescaling, which is a key procedure for comparing apparently incommensurable path weights. An interesting notion of thermal time emerges from this approach.