Non-Gaussian equilibrium distributions arising from the Langevin equation

Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Feb;65(2 Pt 1):021113. doi: 10.1103/PhysRevE.65.021113. Epub 2002 Jan 25.

Abstract

We study the Langevin equation of a point particle driven by random noise, modeled as a two-state Markov process. The corresponding master equation differs from the Fokker-Planck equation. In equilibrium, the velocity of the particle is distributed according to a binomial power law. We discuss transient (i.e., nonequilibrium) behavior, and the consequences of non-Markovian noise statistics.