Gauge optimization of time series for thermal-transport simulations

TL;DR

This paper introduces a gauge optimization method for time series in thermal transport simulations, leveraging gauge invariance to improve statistical analysis of conserved currents.

Contribution

It presents a variational principle based on metric properties of currents to optimize current time series for more accurate transport coefficient evaluation.

Findings

Gauge invariance allows for optimization of current time series.

A variational principle based on metrics improves statistical properties.

Connection to existing data-analysis methods in multi-component systems.

Abstract

Thermal and other transport coefficients were recently shown to be largely independent of the microscopic representation of the energy (current) densities or, more generally, of the relevant conserved densities/currents. In this paper we show how this gauge invariance, which is intimately related to the intrinsic indeterminacy of the energy of isolated atoms, can be exploited to optimize the statistical properties of the current time series from which the transport coefficients can be evaluated. To this end, we make use of a variational principle that relies on the metric properties of the conserved currents, treated as elements of an abstract linear space. Different metrics would result in different variational principles. We finally show how a recently proposed data-analysis methodology based on the theory of transport in multi-component systems can be recovered by a suitable choice of this metric.