Fluctuation theorem in quantum heat conduction

Abstract

We consider steady state heat conduction across a quantum harmonic chain connected to reservoirs modelled by infinite collection of oscillators. The heat, $Q$, flowing across the oscillator in a time interval $τ$ is a stochastic variable and we study the probability distribution function $P(Q)$. In the large $τ$ limit we use the formalism of full counting statistics (FCS) to compute the generating function of $P(Q)$ exactly. We show that $P(Q)$ satisfies the steady state fluctuation theorem (SSFT) regardless of the specifics of system, and it is nongaussian with clear exponential tails. The effect of finite $τ$ and nonlinearity is considered in the classical limit through Langevin simulations. We also obtain predictions of universal heat current fluctuations at low temperatures in clean wires.