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Non-extensive statistical mechanics and generalized Fokker-Planck equation

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  • Plastino, A.R.
  • Plastino, A.

Abstract

A non-linear, generalized Fokker-Planck (GFP) equation is studied whose exact stationary solutions are the maximum entropy distributions introduced by Tsallis in his generalization of Statistical Mechanics. In the case of a constant or linearly varying drift, the time dependent solutions of the GFP equation are seen to obey a suitable form of the celebrated H-theorem. The temporal changes of Tsallis' entropies are seen to be given in terms of the Fisher's information measure. Particular time-dependent solutions of the GFP equation of the maximum (Tsallis') entropy form are obtained.

Suggested Citation

  • Plastino, A.R. & Plastino, A., 1995. "Non-extensive statistical mechanics and generalized Fokker-Planck equation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 222(1), pages 347-354.
    • Handle: RePEc:eee:phsmap:v:222:y:1995:i:1:p:347-354
    DOI: 10.1016/0378-4371(95)00211-1
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    1. Hassan, S.A. & Kuperman, M.N. & Wio, H.S. & Zanette, D.H., 1994. "Evolution of reaction-diffusion patterns in infinite and bounded domains," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 206(3), pages 380-400.
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    Cited by:

    1. Ván, P, 2004. "One- and two-component fluids: restrictions from the Second Law," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 418-426.
    2. Ván, P., 2006. "Unique additive information measures—Boltzmann–Gibbs–Shannon, Fisher and beyond," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 28-33.
    3. dos Santos, M.A.F. & Colombo, E.H. & Anteneodo, C., 2021. "Random diffusivity scenarios behind anomalous non-Gaussian diffusion," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    4. Tsallis, Constantino, 1995. "Non-extensive thermostatistics: brief review and comments," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 221(1), pages 277-290.
    5. Secrest, J.A. & Conroy, J.M. & Miller, H.G., 2020. "A unified view of transport equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 547(C).
    6. Vignat, C. & Lamberti, P.W., 2012. "H-theorems for the Brownian motion on the hyperbolic plane," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 544-551.
    7. Pereira, A.P.P. & Fernandes, J.P. & Atman, A.P.F. & Acebal, J.L., 2018. "Parameter calibration between models and simulations: Connecting linear and non-linear descriptions of anomalous diffusion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 509(C), pages 369-382.
    8. Moretto, Enrico & Pasquali, Sara & Trivellato, Barbara, 2016. "Option pricing under deformed Gaussian distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 446(C), pages 246-263.
    9. Kalogeropoulos, Nikolaos, 2020. "Toward a relative q-entropy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    10. Ji, Lina, 2012. "Conditional Lie–Bäcklund symmetries and invariant subspaces to nonlinear diffusion equations with source," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6320-6331.
    11. Tawfik, Ashraf M. & Elkamash, I.S., 2022. "On the correlation between Kappa and Lévy stable distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 601(C).
    12. Lenzi, E.K. & Ribeiro, M.A. & Fuziki, M.E.K. & Lenzi, M.K. & Ribeiro, H.V., 2018. "Nonlinear diffusion equation with reaction terms: Analytical and numerical results," Applied Mathematics and Computation, Elsevier, vol. 330(C), pages 254-265.
    13. Rodrigues, Ana Flávia P. & Cavalcante, Charles C. & Crisóstomo, Vicente L., 2019. "A projection pricing model for non-Gaussian financial returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 534(C).
    14. da Silva, Sérgio Luiz Eduardo Ferreira & da Costa, Carlos A.N. & Carvalho, Pedro Tiago C. & de Araújo, João Medeiros & dos Santos Lucena, Liacir & Corso, Gilberto, 2020. "Robust full-waveform inversion using q-statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 548(C).

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