Fermionic theory of nonequilibrium steady states

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.