2005/03/14 by Christophe Vignat, C. Vignat, Vignat, C. +2
Economics, Econometrics and Finance · Physics and Astronomy · #Advanced Mathematical Theories and Applications #Complex Systems and Time Series Analysis #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0503337
10 pages, 1 figure
arxiv created 2005/03/14 · openalex publication_date 2005/03/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A finite dimensional-system whose physics is governed by a Gaussian distribution can be regarded as a subsystem of an infinite dimensional-underlying system described by a uniform distribution on the (infinite dimensional) sphere. In turn, a finite dimensional-system ruled by a power-law probability distribution can be considered as a subsystem of a finite underlying system whose physics is governed by a uniform distribution on a finite dimensional sphere. These two uniform distributions (on finite and infinite dimensional spheres) are the most "natural" distributions since they maximize both Tsallis and Shannon entropies without any extra constraint but bounded support. The main advantage of power-law distributions could thus be assigned to the fact that they correspond to a still more "natural" underlying model, namely a finite dimensional sphere. In many physical situations, the underlying system is so large that the distinction between finite and infinite dimension is difficult to see, so that the Boltzmann-Gibbs distribution acquires a great degree of versatility. Moreover, an explicit value of the power-law exponent can be given in terms of the dimension of the underlying model and a geometric interpretation of the temperature-concept is provided.