Second moments of work and heat for a single-particle stochastic heat engine in a breathing harmonic potential

Abstract

Abstract We consider a simple model of a stochastic heat engine, which consists of a single Brownian particle moving in a one-dimensional periodically breathing harmonic potential. The overdamped limit is assumed. Expressions for the second moments (variances and covariances) of heat and work are obtained in the form of integrals, whose integrands contain functions satisfying certain differential equations. The results in the quasi-static limit are simple functions of the temperatures of hot and cold thermal baths. The coefficient of variation of the work is suggested to give an approximate probability for the work to exceed a given threshold. During the derivation, we get the expression of the cumulant-generating function.