The formalism of Kundu et al. [J. Stat. Mech. 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-$\tau$ form of the moment generating function $\langle e^{-\lambda Q}\rangle \approx g\left(\lambda \right)\exp \left[\tau \mu \left(\lambda \right)\right]$, of the total heat flow $Q$ from one of the baths to the particle in a given time interval $\tau$, is studied and exact explicit expressions are obtained for both $\mu \left(\lambda \right)$ and $g\left(\lambda \right)$. 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-$\tau$ 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.

• Received 12 December 2011

DOI:https://doi.org/10.1103/PhysRevE.85.021108