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

Tatsuaki Wada, Antonio M. Scarfone and Hiroshi Matsuzoe

Physica A: Statistical Mechanics and its Applications, 2020, vol. 541, issue C

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.

Keywords: Anomalous transport; κ-deformed Gaussian; Fokker–Planck equation (search for similar items in EconPapers)
Date: 2020
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:541:y:2020:i:c:s0378437119318357

DOI: 10.1016/j.physa.2019.123273

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