System/environment duality of nonequilibrium observables

TL;DR

This paper extends Schnakenberg's theory of nonequilibrium observables to nonsteady states on networks, revealing a duality that exchanges system and environment roles, with applications to entropy production and electromagnetism.

Contribution

It introduces a duality for nonequilibrium observables on networks, generalizes the minimum entropy production principle, and connects discrete electromagnetism to system-environment roles.

Findings

Duality relates system and environment in network observables.

Generalization of minimum entropy production principle in linear regime.

Application to discrete electromagnetism shows field-source exchange.

Abstract

On networks representing probability currents between states of a system, we generalize Schnakenberg's theory of nonequilibrium observables to nonsteady states, with the introduction of a new set of macroscopic observables that, for planar graphs, are related by a duality. We apply this duality to the linear regime, obtaining a dual proposition for the minimum entropy production principle, and to discrete electromagnetism, finding that it exchanges fields with sources. We interpret duality as reversing the role of system and environment, and discuss generalization to nonplanar graphs. The results are based on two theorems regarding the representation of bilinear and quadratic forms over the edge vector space of an oriented graph in terms of observables associated to cycles and cocycles.