Green-Kubo formula for heat conduction in open systems

TL;DR

This paper derives an exact Green-Kubo type formula for heat conduction in open classical Hamiltonian systems coupled to heat baths, applicable to various models and dimensions, and highlights its importance for systems with anomalous heat transport.

Contribution

It introduces an exact Green-Kubo formula for open systems, extending linear response theory to a broader class of heat conduction models.

Findings

Valid for arbitrary dimensions and system sizes.

Applicable to both lattice and fluid models.

Highlights the need for open system formulas in anomalous heat transport.

Abstract

We obtain an exact Green-Kubo type linear response result for the heat current in an open system. The result is derived for classical Hamiltonian systems coupled to heat baths. Both lattice models and fluid systems are studied and several commonly used implementations of heat baths, stochastic as well as deterministic, are considered. The results are valid in arbitrary dimensions and for any system sizes. Our results are useful for obtaining the linear response transport properties of mesoscopic systems. Also we point out that for systems with anomalous heat transport, as is the case in low-dimensional systems, the use of the standard Green-Kubo formula is problematic and the open system formula should be used.