Heat and work fluctuations for a harmonic oscillator

Abstract

The formalism of Kundu [J. Stat. Mech.1742-546810.1088/1742-5468/2011/03/P03007 P03007 (2011)], 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-τ form of the moment generating function <e-λQ>≈g(λ)exp[τμ(λ)], of the total heat flow Q from one of the baths to the particle in a given time interval τ, is studied and exact explicit expressions are obtained for both μ(λ) and g(λ). 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-τ 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.