arXiv 1810.024822018-10cond-mat.stat-mech

On the canonical distributions of a thermal particle in the weakly confining potential of special type

Tatsuaki Wada, Antonio M. Scarfone, Hiroshi Matsuzoe

备注：: 12 pages, 1 figure, resubmitted to JPS but rejected with no scientific reason

英文摘要：

We consider a thermal particle which is diffusing in velocity-space and in a weakly confining potential characterized by the inverse hyperbolic sine function of the particle velocity $v$ and the control parameter $v_c$. The stationary state of the Fokker-Planck equation is shown to be a canonical probability distribution. Furthermore an appropriate re-parametrization relates this stationary state with the $κ$-deformed Gaussian.

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