×

From Gibbs microcanonical ensemble to Tsallis generalized canonical distribution. (English) Zbl 0959.82500

Summary: We derive the Tsallis generalized canonical distribution by recourse to considerations that originate in the traditional Gibbs microcanonical ensemble. The route to be followed has straightforward nature, and only invokes concepts that can be found in any undergraduate textbook on statistical mechanics. It is reasonable to claim, as a consequence, that the Tsallis generalized distribution admits a clear physical interpretation.

MSC:

82B03 Foundations of equilibrium statistical mechanics
82B05 Classical equilibrium statistical mechanics (general)
Full Text: DOI

References:

[1] Jumarie, G. M., Cybern. Syst., 19, 169 (1988) · Zbl 0654.94006
[2] Tsallis, C., J. Stat. Phys., 52, 479 (1988) · Zbl 1082.82501
[3] Curado, E. M.F.; Tsallis, C., J. Phys. A, 25, 1019 (1993) · Zbl 0904.90019
[4] Ito, N.; Tsallis, C., Nuovo Cimento D, 11, 907 (1989)
[5] Andrade, R. F.S., Physica A, 175, 285 (1991)
[6] Mariz, A. M., Phys. Lett. A, 165, 409 (1992)
[7] Ramshaw, J. D., Phys. Lett. A, 175, 169 (1993)
[8] Ramshaw, J. D., Phys. Lett. A, 175, 171 (1993)
[9] Plastino, A. R.; Plastino, A., Phys. Lett. A, 177, 177 (1993)
[10] Plastino, A. R.; Plastino, A., Physica A, 202, 438 (1994) · Zbl 0838.70012
[11] Plastino, A. R.; Plastino, A., Phys. Lett. A, 174, 384 (1993)
[12] Aly, J. J., Minimum energy/maximum entropy states of self-gravitating systems, (Combes, F.; Athanassoula, E., Problem a \(N\) Corps et dynamique gravitationnelle. Problem a \(N\) Corps et dynamique gravitationnelle, Proc. Colloquium at Aussois France (22-26 March 1993), Publications de l’Observatoire de Paris: Publications de l’Observatoire de Paris Paris), 19 · Zbl 0587.76204
[13] A.R. Plastino and A. Plastino, to be published.; A.R. Plastino and A. Plastino, to be published.
[14] Alemany, P. A.; Zanette, D. H., Phys. Rev. E, 49, 956 (1994)
[15] Montroll, E. W.; West, B. J., Fluctuation phenomena (1987), Elsevier: Elsevier Amsterdam
[16] Gibbs, W., Elementary principles in statistical mechanics (1928), Yale Univ. Press: Yale Univ. Press London · JFM 44.0789.10
[17] Reif, F., Fundamentals of statistical and thermal physics (1965), McGraw-Hill: McGraw-Hill New York
[18] Hill, T. L., Introduction to statistical thermodynamics (1960), Addison-Wesley: Addison-Wesley Reading, MA
[19] Chandler, D., Introduction to modern statistical mechanics (1987), Oxford Univ. Press: Oxford Univ. Press Oxford
[20] Feynman, R., Statistical mechanics: A set of lectures (1972), Addison-Wesley: Addison-Wesley Reading, MA · Zbl 0997.82500
[21] Flügge, S., Practical quantum mechanics (1974), Springer: Springer Berlin
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.