Generalized superstatistics of nonequilibrium Markovian systems

TL;DR

This paper develops a superstatistical framework for nonequilibrium Markovian systems using Kirchhoff's diagram technique, representing steady states as superpositions of equilibrium-like channels with detailed balance.

Contribution

It introduces a novel superstatistical approach based on cycle equivalence classes in Markovian systems, extending the description of nonequilibrium steady states.

Findings

Stationary distributions are expressed as sums over channels.

Channels are defined by cycles with zero flux, each satisfying detailed balance.

The approach provides a new perspective on nonequilibrium steady states.

Abstract

The paper is devoted to the construction of the superstatistical description for nonequilibrium Markovian systems. It is based on Kirchhoff's diagram technique and the assumption on the system under consideration to possess a wide variety of cycles with vanishing probability fluxes. The latter feature enables us to introduce equivalence classes called channels within which detailed balance holds individually. Then stationary probability as well as flux distributions are represented as some sums over the channels. The latter construction actually forms the superstatistical description, which, however, deals with a certain superposition of equilibrium subsystems rather then is a formal expansion of the nonequilibrium steady state distribution into terms of the Boltzmann type.