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General thermostatistical formalisms, invariance under uniform spectrum translations, and Tsallis q-additivity

Author

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  • Sisto, R.P.Di
  • Martı́nez, S.
  • Orellana, R.B.
  • Plastino, A.R.
  • Plastino, A.

Abstract

The recent proposal by Tsallis of a generalized thermostatistics devised to treat systems endowed with long-range interactions, long-range memory effects, or a fractal-like relevant phase space, has raised interesting and profound issues concerning the properties of general thermostatistical formalisms. In the present paper we identify families of thermostatistical formalisms that share some fundamental characteristics. The canonical ensemble's invariance under uniform translations of the Hamiltonian's energy spectrum is shown to be a universal property verified by any thermostatistical formalism based upon linear mean energy constraints. We also provide multiparametric families of entropies exhibiting Tsallis q-additivity law.

Suggested Citation

  • Sisto, R.P.Di & Martı́nez, S. & Orellana, R.B. & Plastino, A.R. & Plastino, A., 1999. "General thermostatistical formalisms, invariance under uniform spectrum translations, and Tsallis q-additivity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 265(3), pages 590-613.
    • Handle: RePEc:eee:phsmap:v:265:y:1999:i:3:p:590-613
    DOI: 10.1016/S0378-4371(98)00561-5
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    Cited by:

    1. Suyari, Hiroki, 2006. "Mathematical structures derived from the q-multinomial coefficient in Tsallis statistics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 368(1), pages 63-82.
    2. Oikonomou, Th., 2007. "Tsallis, Rényi and nonextensive Gaussian entropy derived from the respective multinomial coefficients," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 386(1), pages 119-134.

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