Heat statistics in the relaxation process of the Edwards-Wilkinson elastic manifold

TL;DR

This paper analytically investigates the heat statistics during the relaxation of the Edwards-Wilkinson elastic manifold, a continuous stochastic field with infinite degrees of freedom, revealing scaling behaviors and large deviation properties.

Contribution

It extends stochastic thermodynamics to infinite-dimensional systems by providing exact solutions for heat statistics in the Edwards-Wilkinson model.

Findings

Heat cumulants scale with time and system size.

Large deviation rate function characterizes heat fluctuations.

Ultraviolet divergence requires a cutoff for cumulant calculations.

Abstract

The stochastic thermodynamics of systems with a few degrees of freedom has been studied extensively so far. We would like to extend the study to systems with more degrees of freedom and even further-continuous fields with infinite degrees of freedom. The simplest case for a continuous stochastic field is the Edwards-Wilkinson elastic manifold. It is an exactly solvable model of which the heat statistics in the relaxation process can be calculated analytically. The cumulants require a cutoff spacing to avoid ultra-violet divergence. The scaling behavior of the heat cumulants with time and the system size as well as the large deviation rate function of the heat statistics in the large size limit is obtained.