The q-exponential family in statistical physics
Faculty of Sciences. Physics
Journal of physics : conference series. - Bristol
Proceedings of Kyoto RIMS Workshop Mathematical Aspects of Generalized Entropies and their Applications / Suyari, H. [edit.]; et al. [edit.]
, p. 012003,1-012003,11
University of Antwerp
The Boltzmann-Gibbs probability distribution, seen as a statistical model, belongs to the exponential family. Recently, the latter concept has been generalized. The q-exponential family has been shown to be relevant for the statistical description of small isolated systems. Two main applications are reviewed: 1. The distribution of the momentum of a single particle is a q-Gaussian, the distribution of its velocity is a deformed Maxwellian; 2. The configurational density distribution belongs to the q-exponential family. The definition of the temperature of small isolated systems is discussed. It depends on defining the thermodynamic entropy of a microcanonical ensemble in a suitable manner. The simple example of non-interacting harmonic oscillators shows that Rényi's entropy functional leads to acceptable results.