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

Author

Listed:
  • Wada, Tatsuaki
  • Scarfone, Antonio M.
  • Matsuzoe, Hiroshi

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.

Suggested Citation

  • Wada, Tatsuaki & Scarfone, Antonio M. & Matsuzoe, Hiroshi, 2020. "On the canonical distributions of a thermal particle in a generalized velocity-dependent potential," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 541(C).
    • Handle: RePEc:eee:phsmap:v:541:y:2020:i:c:s0378437119318357
    DOI: 10.1016/j.physa.2019.123273
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