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Poincaré's observation and the origin of Tsallis generalized canonical distributions

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  • Vignat, C.
  • Plastino, A.

Abstract

In this paper, we present some geometric properties of the maximum entropy Tsallis-distributions under energy constraint. In the case q>1, these distributions are proved to be marginals of uniform distributions on the sphere; in the case q<1, they can be constructed as conditional distributions of a Cauchy law built from the same uniform distribution on the sphere using a gnomonic projection. As such, these distributions reveal the relevance of using Tsallis distributions in the microcanonical setup: an example of such application is given in the case of the ideal gas.

Suggested Citation

  • Vignat, C. & Plastino, A., 2006. "Poincaré's observation and the origin of Tsallis generalized canonical distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 365(1), pages 167-172.
    • Handle: RePEc:eee:phsmap:v:365:y:2006:i:1:p:167-172
    DOI: 10.1016/j.physa.2006.01.028
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    References listed on IDEAS

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    1. Adib, Artur B. & Moreira, André A. & Andrade Jr, José S. & Almeida, Murilo P., 2003. "Tsallis thermostatistics for finite systems: a Hamiltonian approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 322(C), pages 276-284.
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    Cited by:

    1. Arismendi, Juan & Genaro, Alan De, 2016. "A Monte Carlo multi-asset option pricing approximation for general stochastic processes," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 75-99.

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