The nonlinear Fokker-Planck equation with nongradient drift forces and an anisotropic potential.

Studies regarding physical phenomena described by nonlinear Fokker-Planck equations usually consider the case where the drift forces acting on the physical system under investigation are derived from the gradient of a potential function. In the present manuscript, we investigate nonlinear Fokker-Planck equations, where the drift field has a component that is derived from the gradient of an asymmetric potential and another that corresponds to a nongradient force term. We consider the specific case of a two-dimensional, nonlinear Fokker-Planck equation where the drift field is obtained from an anisotropic, harmonic potential, besides the nongradient term.

Entropy Optimization, Generalized Logarithms, and Duality Relations.

Several generalizations or extensions of the Boltzmann-Gibbs thermostatistics, based on non-standard entropies, have been the focus of considerable research activity in recent years. Among these, the power-law, non-additive entropies Sq≡k1-∑ipiqq-1(q∈R;S1=SBG≡-k∑ipilnpi) have harvested the largest number of successful applications. The specific structural features of the Sq thermostatistics, therefore, are worthy of close scrutiny.

Statistical dynamics of driven systems of confined interacting particles in the overdamped-motion regime.

Systems consisting of confined, interacting particles doing overdamped motion admit an effective description in terms of nonlinear Fokker-Planck equations. The behavior of these systems is closely related to the power-law entropies and can be interpreted in terms of the -based thermostatistics. The connection between overdamped systems and the measures provides valuable insights on diverse physical problems, such as the dynamics of interacting vortices in type-II superconductors.

Nonlinear Fokker-Planck Equation Approach to Systems of Interacting Particles: Thermostatistical Features Related to the Range of the Interactions.

Nonlinear Fokker-Planck equations (NLFPEs) constitute useful effective descriptions of some interacting many-body systems. Important instances of these nonlinear evolution equations are closely related to the thermostatistics based on the S q power-law entropic functionals. Most applications of the connection between the NLFPE and the S q entropies have focused on systems interacting through short-range forces.

Multispecies effects in the equilibrium and out-of-equilibrium thermostatistics of overdamped motion.

Progress has been recently made, both theoretical and experimental, regarding the thermostatistics of complex systems of interacting particles or agents (species) obeying a nonlinear Fokker-Planck dynamics. However, major advances along these lines have been restricted to systems consisting of only one type of species. The aim of the present contribution is to overcome that limitation, going beyond single-species scenarios.