Heat and work fluctuations for a harmonic oscillator

TL;DR

This paper applies a formalism to analyze heat and work fluctuations in a harmonic oscillator system, deriving exact large deviation functions and probability distributions for heat flow and work in different thermal setups.

Contribution

It provides explicit analytical expressions for the large deviation functions of heat and work in harmonic systems, extending previous theoretical frameworks.

Findings

Exact large deviation functions for heat flow are derived.

Complete asymptotic forms of work probability density are obtained.

The formalism is applied to a single Brownian particle in a harmonic trap.

Abstract

The formalism of Kundu et al. [J. Stat. Mech. (2011) P03007], for computing the large deviations of heat flow in harmonic systems, is applied to the case of single Brownian particle in a harmonic trap and coupled to two heat baths at different temperatures. The large-t form of the moment generating function <exp[-sQ]> ~ g(s) exp[t m(s)], of the total heat flow Q from one of the baths to the particle in a given time interval t, is studied and exact explicit expressions are obtained for both m(s) and g(s). For a special case of the single particle problem that corresponds to the work done by an external stochastic force on a harmonic oscillator coupled to a thermal bath, the large-t form of the moment generating function is analyzed to obtain the exact large deviation function as well as the complete asymptotic forms of the probability density function of the work.