Nonlinear inhomogeneous Fokker-Planck equations: entropy and free-energy time evolution

Abstract

We extend a recently introduced free-energy formalism for homogeneous Fokker-Planck equations to a wide, and physically appealing, class of inhomogeneous nonlinear Fokker-Planck equations. In our approach, the free-energy functional is expressed in terms of an entropic functional and an auxiliary potential, both derived from the coefficients of the equation. With reference to the introduced entropic functional, we discuss the entropy production in a relaxation process towards equilibrium. The properties of the stationary solutions of the considered Fokker-Planck equations are also discussed.

arXiv comment8 pages

References in corpus (19)

• Stochastic thermodynamics, fluctuation theorems, and molecular machines
• Macroscopic fluctuation theory
• Non Linear Kinetics underlying Generalized Statistics
• Anomalous diffusion in the presence of external forces: exact time-dependent solutions and entropy
• Stochastic thermodynamics: Principles and perspectives
• State-dependent diffusion: thermodynamic consistency and its path integral formulation
• Option Pricing Formulas based on a non-Gaussian Stock Price Model
• Generalized thermodynamics and Fokker-Planck equations. Applications to stellar dynamics, two-dimensional turbulence and Jupiter's great red spot
• Thermostatistics of overdamped motion of interacting particles
• Nonlinear mean field Fokker-Planck equations. Application to the chemotaxis of biological populations
• Experimental validation of nonextensive scaling law in confined granular media
• Consequences of the H-Theorem from Nonlinear Fokker-Planck Equations
• A General Nonlinear Fokker-Planck Equation and its Associated Entropy
• Strictly and asymptotically scale-invariant probabilistic models of $N$ correlated binary random variables having {\em q}--Gaussians as $N\to \infty$ limiting distributions
• Microscopic dynamics underlying the anomalous diffusion
• Thermodynamic transformations of nonequilibrium states
• Nonlinear inhomogeneous Fokker-Planck equation within a generalized Stratonovich prescription
• General continuum approach for dissipative systems of repulsive particles
• On the robustness of the $q$-Gaussian family

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• Microscopic Dynamics of Nonlinear Fokker-Planck Equations
• Stationary solution and $H$ theorem for a generalized Fokker-Planck equation
• Characterization of the non-Arrhenius behavior of supercooled liquids by modeling non-additive stochastic systems
• A unified framework for divergences, free energies, and Fokker-Planck equations