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

C. VIGNAT; ANGEL LUIS PLASTINO

PHYSICA A - STATISTICAL AND THEORETICAL PHYSICS

Elsevier

Lugar: Amsterdam; Año: 2006 vol. 365 p. 167 - 172

0378-4371

  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. 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. 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. 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. 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. 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. 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.