Poincaré's Observation and the Origin of Tsallis Generalized Canonical Distributions

Details Poincaré's Observation and the Origin of Tsallis Generalized Canonical Distributions Poincaré's Observation and the Origin of Tsallis Generalized Canonical Distributions

2005-09-27

arxiv.org/abs/cond-mat/0509689v1

Physics

Condensed Matter

Statistical Mechanics

2 figures

Scientific paper

10.1016/j.physa.2006.01.028

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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