Non-additive entropies and quantum statistics

Abstract The properties of general non-additive entropic forms and their emergence in quantum statistical mechanics are discussed. As particular examples, we analyze the entropies associated with general exponential distributions as well as those related with independent particles satisfying Fermi, Bose and fractional exclusion statistics.

[1]  Michel Loève,et al.  Probability Theory I , 1977 .

[2]  R. S. Mendes,et al.  Blackbody radiation in nonextensive Tsallis statistics: Exact solution , 1998 .

[3]  G. A. Raggio,et al.  Remarks on “Thermodynamic stability conditions for the Tsallis and Rényi entropies” by Ramshaw , 1996 .

[4]  Haldane,et al.  "Fractional statistics" in arbitrary dimensions: A generalization of the Pauli principle. , 1991, Physical review letters.

[5]  Loh,et al.  Generalization of the Planck radiation law and application to the cosmic microwave background radiation. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[6]  C. Tsallis,et al.  Statistical-mechanical foundation of the ubiquity of Lévy distributions in Nature. , 1995, Physical review letters.

[7]  C. Tsallis.  Possible generalization of Boltzmann-Gibbs statistics , 1988 .

[8]  C. Beck,et al.  Thermodynamics of chaotic systems : an introduction , 1993 .

[9]  C. Beck,et al.  Thermodynamics of chaotic systems , 1993 .

[10]  R. Rossignoli,et al.  Fluctuations and Odd-Even Effects in Small Superfluid Systems , 1999 .

[11]  A. Polychronakos.  Probabilities and path-integral realization of exclusion statistics , 1995, hep-th/9503077.

[12]  A. Plastino.  On the universality of thermodynamics' Legendre transform structure , 1997 .

[13]  R. S. Mendes.  Some general relations in arbitrary thermostatistics , 1997 .

[14]  C. Tsallis,et al.  Nonextensivity and Multifractality in Low-Dimensional Dissipative Systems , 1997, cond-mat/9709226.

[15]  Kim,et al.  Crossover from extensive to nonextensive behavior driven by long-range interactions. , 1995, Physical review. B, Condensed matter.

[16]  Aleksandr Yakovlevich Khinchin,et al.  Mathematical foundations of information theory , 1959 .

[17]  Nonextensive thermostatistics and deformed structures , 1998 .

[18]  R. Rossignoli,et al.  Thermal and Quantal Fluctuations for Fixed Particle Number in Finite Superfluid Systems , 1998 .