Generalized Ensemble Theory with Non-extensive Statistics

Abstract

The non-extensive canonical ensemble theory is reconsidered with the method of Lagrange multipliers by maximizing Tsallis entropy, with the constraint that the normalized term of Tsallis' $q-$average of physical quantities, the sum $\sum p_j^q$, is independent of the probability $p_i$ for Tsallis parameter $q$. The self-referential problem in the deduced probability and thermal quantities in non-extensive statistics is thus avoided, and thermodynamical relationships are obtained in a consistent and natural way. We also extend the study to the non-extensive grand canonical ensemble theory and obtain the $q$-deformed Bose-Einstein distribution as well as the $q$-deformed Fermi-Dirac distribution. The theory is further applied to the generalized Planck law to demonstrate the distinct behaviors of the various generalized $q$-distribution functions discussed in literature.

14 pages, 2 figures

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Cited by in corpus (5)

• The nonextensive statistical ensembles with dual thermodynamic interpretations
• Chiral phase transition within the linear sigma model in the Tsallis nonextensive statistics based on density operator
• Relation between the escort average in microcanonical ensemble and the escort average in canonical ensemble in the Tsallis statistics
• An alternative method for solving the Gaussian integral
• A note on the connection between non-additive entropy and $h$-derivative