Thermostats, chaos and Onsager reciprocity

TL;DR

This paper explores the relationship between phase space contraction, fluctuation theorem, and Green-Kubo relations in nonequilibrium statistical mechanics, highlighting how metric choices affect these connections and extending their applicability.

Contribution

It demonstrates that the link between the fluctuation theorem and Green-Kubo formulas is more general than previously thought, influenced by the choice of phase space metric.

Findings

Phase space contraction can be independent of forcing parameters.

Changing the phase space metric alters phase space contraction.

The fluctuation theorem and Green-Kubo relations are more broadly connected than prior assumptions.

Abstract

Finite thermostats are studied in the context of nonequilibrium statistical mechanics. Entropy production rate has been identified with the mechanical quantity expressed by the phase space contraction rate and the currents have been linked to its derivatives with respect to the parameters measuring the forcing intensities. In some instances Green-Kubo formulae, hence Onsager reciprocity, have been related to the fluctuation theorem. However, mainly when dissipation takes place at the boundary (as in gases or liquids in contact with thermostats), phase space contraction may be independent on some of the forcing parameters or, even in absence of forcing, phase space contraction may not vanish: then the relation with the fluctuation theorem does not seem to apply. On the other hand phase space contraction can be altered by changing the metric on phase space: here this ambiguity is discussed and employed to show that the relation between the fluctuation theorem and Green-Kubo formulae can be extended and is, by far, more general.