Nonequilibrium temperature response for stochastic overdamped systems

TL;DR

This paper develops a novel theoretical framework to analyze the temperature response of nonequilibrium overdamped Langevin systems, introducing regularization techniques and applying them to define nonequilibrium heat capacity and thermal expansion.

Contribution

It derives a linear response theory for noise perturbations in nonequilibrium systems and introduces a path-integral regularization method for divergent terms.

Findings

Derived the response to noise intensity perturbations

Introduced a regularization method for divergent quadratic responses

Numerical examples demonstrate nonequilibrium heat capacity and thermal expansion

Abstract

The thermal response of nonequilibrium systems requires the knowledge of concepts that go beyond entropy production. This is showed for systems obeying overdamped Langevin dynamics, either in steady states or going through a relaxation process. Namely, we derive the linear response to perturbations of the noise intensity, mapping it onto the quadratic response to a constant small force. The latter, displaying divergent terms, is explicitly regularized with a novel path-integral method. The nonequilibrium equivalents of heat capacity and thermal expansion coefficient are two applications of this approach, as we show with numerical examples.