Generating function formula of heat transfer in harmonic networks

Abstract

We consider heat transfer across an arbitrary classical harmonic network connected to two heat baths at different temperatures. The network has N positional degrees of freedom, of which N_L are connected to a bath at temperature T_L and N_R are connected to a bath at temperature T_R. We derive an exact formula for the cumulant generating function for heat transfer between the two baths. The formula is valid even for NL≠NR and satisfies the Gallavotti-Cohen fluctuation symmetry. Since harmonic crystals in three dimensions are known to exhibit different regimes of transport such as ballistic, anomalous, and diffusive, our result implies validity of the fluctuation theorem in all regimes. Our exact formula provides a powerful tool to study other properties of nonequilibrium current fluctuations.