General nonlinear Fokker-Planck equations with multiple potentials: H-theorem and constraints
Faculty of Science, Kanagawa University, 2946, 6-233 Tsuchiya, Hiratsuka, 259-1293, Kanagawa, Japan
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Accepted: 10 September 2018
Published online: 25 October 2018
In one of the most general possible forms of nonlinear Fokker-Planck equations in one-dimensional space, we consider systems under multiple external potentials with a single diffusion term. We prove the associated H-theorem: that is, the free-energy functional decreases in time under a suitable condition, which relates the entropic form and the two nonlinear functionals in the equations. We consider the constraint on the entropic form and provide a constraint on the functional contained in the diffusion term. Moreover, we see that the gauge field associated with this type of general nonlinear Fokker-Planck equations represents an indicator for fluctuations of the probability flux velocity.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2018