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Families of Fokker-Planck equations and the associated entropic form for a distinct steady-state probability distribution with a known external force field
Phys. Rev. E 91, 022104 – Published 5 February, 2015
DOI: https://doi.org/10.1103/PhysRevE.91.022104
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.
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