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' average of physical quantities, the sum , is independent of the probability for Tsallis parameter . 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 -deformed Bose-Einstein distribution as well as the -deformed Fermi-Dirac distribution. The theory is further applied to the generalized Planck law to demonstrate the distinct behaviors of the various generalized -distribution functions discussed in literature.
Cite
@article{arxiv.1707.03526,
title = {Generalized Ensemble Theory with Non-extensive Statistics},
author = {Ke-Ming Shen and Ben-Wei Zhang and En-Ke Wang},
journal= {arXiv preprint arXiv:1707.03526},
year = {2017}
}
Comments
14 pages, 2 figures