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Generalized thermostatistics and mean-field theory

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  • Naudts, Jan

Abstract

The present paper studies a large class of temperature-dependent probability distributions and shows that entropy and energy can be defined in such a way that these probability distributions are the equilibrium states of a generalized thermostatistics, which is obtained from the standard formalism by deformation of exponential and logarithmic functions. Since this procedure is non-unique, specific choices are motivated by showing that the resulting theory is well-behaved. In particular, with the choices made in the present paper, the equilibrium state of any system with a finite number of degrees of freedom is, automatically, thermodynamically stable and satisfies the variational principle.

Suggested Citation

  • Naudts, Jan, 2004. "Generalized thermostatistics and mean-field theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 332(C), pages 279-300.
    • Handle: RePEc:eee:phsmap:v:332:y:2004:i:c:p:279-300
    DOI: 10.1016/j.physa.2003.10.013
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    References listed on IDEAS

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    1. Tsallis, Constantino & Mendes, RenioS. & Plastino, A.R., 1998. "The role of constraints within generalized nonextensive statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 261(3), pages 534-554.
    2. Naudts, Jan, 2002. "Deformed exponentials and logarithms in generalized thermostatistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 323-334.
    3. Kaniadakis, G., 2001. "Non-linear kinetics underlying generalized statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 296(3), pages 405-425.
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    Cited by:

    1. Vignat, Christophe & Naudts, Jan, 2005. "Stability of families of probability distributions under reduction of the number of degrees of freedom," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 350(2), pages 296-302.
    2. Naudts, Jan, 2004. "Generalized thermostatistics based on deformed exponential and logarithmic functions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 340(1), pages 32-40.

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