Families of Fokker-Planck equations and the associated entropic form for a distinct steady-state probability distribution with a known external force field

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
Somayeh Asgarani

Abstract

A method of finding entropic form for a given stationary probability distribution and specified potential field is discussed, using the steady-state Fokker-Planck equation. As examples, starting with the Boltzmann and Tsallis distribution and knowing the force field, we obtain the Boltzmann-Gibbs and Tsallis entropies. Also, the associated entropy for the gamma probability distribution is found, which seems to be in the form of the gamma function. Moreover, the related Fokker-Planck equations are given for the Boltzmann, Tsallis, and gamma probability distributions.

References

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Oct 25, 2000·Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics·S Primak
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Sep 26, 2012·Physical Review Letters·O E Garcia

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Citations

Jan 14, 2017·Physical Review. E·R S WedemannC Tsallis
Aug 17, 2018·Physical Review. E·A R PlastinoC Tsallis

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