Fermionic theory of nonequilibrium steady states

TL;DR

This paper develops a fermionic theoretical framework for analyzing nonequilibrium steady states in Markovian systems, extending statistical mechanics concepts and revealing a supersymmetric field theory structure.

Contribution

It introduces a fermionic approach to nonequilibrium steady states, generalizing Boltzmann-Gibbs mechanics and identifying a supersymmetry-breaking field theory description.

Findings

Response to perturbations can be explicitly computed.

Ensembles of steady states are described by a 2D supersymmetric field theory.

Potential for developing solvable models of nonequilibrium systems.

Abstract

As the quantification of metabolism, nonequilibrium steady states play a central role in living matter, but are beyond the purview of equilibrium statistical mechanics. Here we develop a fermionic theory of nonequilibrium steady states in continuous-time Markovian systems, generalizing Boltzmann-Gibbs statistical mechanics to this case. The response to an arbitrary perturbation is computed, and simplified in canonical cases. Beyond response, we consider ensembles of nonequilibrium steady states and show that a general class of ensembles is described by a 2D statistical field theory with infinitesimally broken supersymmetry, which may form the basis of nontrivial solvable models of nonequilibrium steady states.