Free energies based on generalized entropies and H-theorems for nonlinear Fokker–Planck equations

The relationship between H-theorems and free energies is studied on the basis of generalized entropies. Two kinds of nonlinear Fokker–Planck equations with different nonlinear diffusion terms that exhibit the power-law-type equilibrium distributions of Tsallis thermostatistics are investigated from the viewpoint of nonequilibrium free energies and stability analysis of their solutions. Using the generalized entropies Liapunov functions are constructed to show H-theorems, which ensure uniqueness of and convergence to the equilibrium distributions of the nonlinear Fokker–Planck equations.