2010/03/18 by Jean Pierre Boon, J. P. Boon, Boon, J. P. +3
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Complex Systems and Time Series Analysis #FOS: Physical sciences #Fractional Differential Equations Solutions #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #cond-mat.stat-mech #math-ph #math.MP
paper · pdf · doi:10.48550/arxiv.1003.3592
Updated version with new title and new presentation; no changes in the mathematical analysis
openalex publication_date 2010/03/18 · arxiv created 2010/06/30 · arxiv updated 2010/07/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The homogeneous entropy for continuous systems in nonextensive statistics reads SHq=kB (1 - (K ∫ dΓρ1/q(Γ))q)/(1-q), where Γ is the phase space variable. Optimization of SHq combined with normalization and energy constraints gives an implicit expression of the distribution function ρ(Γ) which can be computed explicitly for the ideal gas. From this result, we compute properties such as the energy fluctuations and the specific heat. Similar results are also presented using the formulation based on the Tsallis entropy. From the analysis, we discuss the validity of the application of the nonextensive formalism to continuous Hamiltonian systems which is found to be restricted to the range q<1, which renders problematic its applicability to the class of phenomena exhibiting power law decay.