Poincaré's Observation and the Origin of Tsallis Generalized Canonical Distributions
arXiv:cond-mat/0509689 · doi:10.1016/j.physa.2006.01.028
Abstract
In this paper, we present some geometric properties of the maximum entropy (MaxEnt) Tsallis- distributions under energy constraint. In the case q > 1, these distributions are proved to be marginals of uniform distributions on the sphere; in the case q < 1, they can be constructed as conditional distribu- tions of a Cauchy law built from the same uniform distribution on the sphere using a gnomonic projection. As such, these distributions reveal the relevance of using Tsallis distributions in the microcanonical setup: an example of such application is given in the case of the ideal gas.
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