Heat leakage in overdamped harmonic systems

TL;DR

This paper analyzes heat leakage phenomena in overdamped harmonic systems, revealing limitations of the overdamped approximation in accurately capturing stochastic heat exchanges during temperature changes.

Contribution

It provides exact calculations of heat exchanges in overdamped and underdamped regimes and uncovers the origin of heat leakage related to initial velocity relaxation.

Findings

Underdamped heat reduces to overdamped in large friction during isothermal processes.

Overdamped approximation fails to accurately describe heat during isochoric transformations.

Heat leakage originates from initial velocity relaxation of the system.

Abstract

We investigate the occurrence of heat leakages in overdamped Brownian harmonic systems. We exactly compute the underdamped and overdamped stochastic heats exchanged with the bath for a sudden frequency or temperature switch. We show that the underdamped heat reduces to the corresponding overdamped expression in the limit of large friction for the isothermal process. However, we establish that this is not the case for the isochoric transformation. We microscopically derive the additionally generated heat leakage and relate its origin to the initial relaxation of the velocity of the system. Our results highlight the limitations of the overdamped approximation for the evaluation of the stochastic heat in systems with changing bath temperature.