Fluctuation theorem in quantum heat conduction

TL;DR

This paper analyzes quantum heat conduction in a harmonic chain, deriving the exact probability distribution of heat flow, confirming the fluctuation theorem, and exploring effects of finite time and nonlinearity.

Contribution

It provides an exact computation of the heat flow distribution in a quantum harmonic chain and confirms the steady state fluctuation theorem in this context.

Findings

Probability distribution P(Q) is non-Gaussian with exponential tails.

P(Q) satisfies the steady state fluctuation theorem universally.

Finite time and nonlinearity effects are studied via classical Langevin simulations.

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 $\tau$ is a stochastic variable and we study the probability distribution function $P(Q)$. In the large $\tau$ 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 $\tau$ 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.