2012/06/22 by Nikos Kalogeropoulos, Kalogeropoulos, Nikos · 1 citation
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Complex Systems and Time Series Analysis #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #cond-mat.stat-mech #gr-qc #hep-th #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1206.5127
12 pages, No figures, Standard LaTeX2e
arxiv created 2012/06/22 · openalex publication_date 2012/06/22 · arxiv updated 2012/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We present an argument justifying the origin of the escort distributions used in calculations involving the Tsallis entropy. We rely on an induced hyperbolic Riemannian metric reflecting the generalized composition property of the Tsallis entropy. The mapping of the corresponding Riemannian measure on the space of thermodynamic variables gives the specific form of the escort distributions and provides a geometric interpretation of the non-extensive parameter. In addition, we explain the polynomial rate of increase of the sample space volume for systems described by the Tsallis entropy, thus extending the previously reached conclusions for discrete systems to the case of systems whose evolution is described by flows on Riemannian manifolds.