title: Curl forces and the nonlinear Fokker-Planck equation.
abstract: Nonlinear Fokker-Planck equations endowed with curl drift forces are investigated. The conditions under which these evolution equations admit stationary solutions, which are q exponentials of an appropriate potential function, are determined. It is proved that when these stationary solutions exist, the nonlinear Fokker-Planck equations satisfy an H theorem in terms of a free-energy-like quantity involving the S_{q} entropy. A particular two-dimensional model admitting analytical, time-dependent q-Gaussian solutions is discussed in detail. This model describes a system of particles with short-range interactions, performing overdamped motion under drag effects due to a rotating resisting medium. It is related to models that have been recently applied to the study of type-II superconductors. The relevance of the present developments to the study of complex systems in physics, astronomy, and biology is discussed.
authors.affiliation: Instituto de Matemática e Estatística, Universidade do Estado do Rio de Janeiro, Rua São Francisco Xavier 524, 20550-900 Rio de Janeiro, Rio de Janeiro, Brazil.
authors.forename: R S
authors.initials: RS
authors.lastname: Wedemann
authors.affiliation: CeBio y Secretaría de Investigación, Universidad Nacional del Noroeste de la Província de Buenos Aires, UNNOBA, CONICET, Roque Saenz Peña 456, Junín, 2700 Buenos Aires, Argentina.
authors.forename: A R
authors.initials: AR
authors.lastname: Plastino
authors.affiliation: Centro Brasileiro de Pesquisas Físicas and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150, 22290-180 Rio de Janeiro, Rio de Janeiro, Brazil.|Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA.
authors.forename: C
authors.initials: C
authors.lastname: Tsallis