title: Probability distributions and associated nonlinear Fokker-Planck equation for the two-index entropic form S(q,δ).
abstract: The probability distributions and associated Fokker-Planck equation of the recently postulated entropic form, S(q,δ), are investigated. This entropy was proposed as an unification of the well-known S(q) of nonextensive-statistical mechanics and S(δ), which appeared lately as a possibly appropriate candidate for the black-hole entropy. The connection between S(q,δ) and a nonlinear Fokker-Planck equation, such as to satisfy an H-theorem, is explored. The stationary-state probability distribution follows a transcendental equation, which is solved numerically for typical values of q and δ. The same transcendental equation is obtained through the maximum-entropy principle, showing that the two procedures are equivalent.
authors.affiliation: Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150 22290-180, Rio de Janeiro, RJ, Brazil.
authors.forename: Mauricio S
authors.initials: MS
authors.lastname: Ribeiro
authors.affiliation: Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150 22290-180, Rio de Janeiro, RJ, Brazil and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150 22290-180, Rio de Janeiro, RJ, Brazil.
authors.forename: Fernando D
authors.initials: FD
authors.lastname: Nobre
authors.affiliation: Centro Brasileiro de Pesquisas Físicas, Rua Xavier Sigaud 150 22290-180, Rio de Janeiro, RJ, Brazil and National Institute of Science and Technology for Complex Systems, Rua Xavier Sigaud 150 22290-180, Rio de Janeiro, RJ, Brazil and Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, New Mexico 87501, USA.
authors.forename: Constantino
authors.initials: C
authors.lastname: Tsallis