On the canonical distributions of a thermal particle in a generalized velocity-dependent potential

Abstract

We consider a thermal particle diffusing in velocity-space under a generalized velocity-dependent potential characterized by the inverse hyperbolic sine function of the particle velocity v and the control parameter vc. This velocity-dependent potential can be considered as a deformation of Rayleigh’s dissipation function. The stationary state of the corresponding Fokker–Planck equation is shown to be a canonical probability distribution. Furthermore an appropriate re-parameterization relates this stationary state with the κ-deformed Gaussian. A possible interpretation of the deformation parameter κ is proposed.