Counting statistics of energy transport across squeezed thermal reservoirs

Abstract

A general formalism for computing the full counting statistics of energy exchanged between “N” squeezed thermal photon reservoirs weakly coupled to a cavity with “M” photon modes is presented. The formalism is based on the two-point measurement scheme and is applied to two simple special cases: the relaxation dynamics of a single mode cavity in contact with a single squeezed thermal photon reservoir and the steady-state energy transport between two squeezed thermal photon reservoirs coupled to a single cavity mode. Using analytical results, it is found that the short time energy exchange statistics is significantly affected by noncommutativity of the initial energy measurements with the reservoirs' squeezed states, and may lead to negative probabilities if not accounted for properly. Furthermore, it is found that for the single reservoir setup, generically there is no transient or steady-state Jarzynski-Wójcik energy exchange fluctuation theorem. In contrast, for the two reservoir cases, although there is no generic transient energy exchange fluctuation theorem, a steady-state energy exchange fluctuation theorem with a nonuniversal affinity is found to be valid. Statistics of energy currents are further discussed.