Generalized superstatistics of nonequilibrium Markovian systems

Physica A: Statistical Mechanics and its Applications. 2009. Vol. 388. No. 21. P. 4535–4550.

Lubashevsky I., Friedrich R., Heuer A., Ushakov A.

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 than a formal expansion of the nonequilibrium steady state distribution into terms of the Boltzmann type.

Keywords: Markovian process, quasistatistics