Poincaré's observation and the origin of Tsallis generalized canonical distributions

✍ Scribed by C. Vignat; A. Plastino

• Publisher: Elsevier Science
• Year: 2006
• Tongue: English
• Weight: 168 KB
• Volume: 365
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/j.physa.2006.01.028

✦ Synopsis

In this paper, we present some geometric properties of the maximum entropy Tsallis-distributions under energy constraint. In the case q41, these distributions are proved to be marginals of uniform distributions on the sphere; in the case qo1, they can be constructed as conditional distributions 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.