Generating Function Formula of Heat Transfer in Harmonic Networks

TL;DR

This paper derives an exact formula for the cumulant generating function of heat transfer in harmonic networks, applicable to various transport regimes, and confirms the fluctuation theorem's validity in these systems.

Contribution

The paper presents a novel exact formula for heat transfer cumulant generating functions in harmonic networks, extending understanding across different transport regimes.

Findings

Formula valid for networks with unequal heat bath connections

Satisfies Gallavotti-Cohen fluctuation symmetry

Applicable to ballistic, anomalous, and diffusive regimes

Abstract

We consider heat transfer across an arbitrary 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 $N_L \ne N_R$ 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.