Gauge invariance of thermal transport coefficients

TL;DR

This paper demonstrates that thermal transport coefficients are gauge invariant, meaning they are independent of the microscopic energy density expressions, due to energy conservation and extensivity, confirmed numerically for a Lennard-Jones fluid.

Contribution

It establishes a gauge invariance principle for thermal transport coefficients and verifies it through numerical simulations, highlighting their independence from microscopic energy density choices.

Findings

Different microscopic energy densities yield the same thermal conductivity.

The gauge invariance is rooted in energy conservation and extensivity.

Numerical validation performed on a Lennard-Jones fluid.

Abstract

Thermal transport coefficients are independent of the specific microscopic expression for the energy density and current from which they can be derived through the Green-Kubo formula. We discuss this independence in terms of a kind of gauge invariance resulting from energy conservation and extensivity, and demonstrate it numerically for a Lennard-Jones fluid, where different forms of the microscopic energy density lead to different time correlation functions for the heat flux, all of them, however, resulting in the same value for the thermal conductivity.