Curl forces and the nonlinear Fokker-Planck equation

R. S. Wedemann, A. R. Plastino, and C. Tsallis
Phys. Rev. E 94, 062105 – Published 2 December 2016

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 Sq 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.

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  • Received 12 September 2016
  • Revised 13 November 2016

DOI:https://doi.org/10.1103/PhysRevE.94.062105

©2016 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & Thermodynamics

Authors & Affiliations

R. S. Wedemann1,*, A. R. Plastino2,†, and C. Tsallis3,4,‡

  • 1Instituto 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
  • 2CeBio 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
  • 3Centro 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
  • 4Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA

  • *roseli@ime.uerj.br
  • arplastino@unnoba.edu.ar
  • tsallis@cbpf.br

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Issue

Vol. 94, Iss. 6 — December 2016

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