2015/01/11 by Uǧur Tırnaklı, Ugur Tirnakli, Ernesto P. Borges · 4 citations
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Boltzmann distribution #Complex Systems and Time Series Analysis #Ergodic theory #Ergodicity #Mathematical analysis #Mathematics #Physics #Quantum chaos and dynamical systems #Statistical Mechanics and Entropy #Statistical physics #Statistics #Tsallis statistics #cond-mat.stat-mech
paper · pdf · doi:10.1038/srep23644
published as Sci. Rep. 6, 23644 (2016)
arxiv created 2015/01/11 · openalex publication_date 2016/03/23 · arxiv updated 2016/05/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
As well known, Boltzmann-Gibbs statistics is the correct way of thermostatistically approaching ergodic systems. On the other hand, nontrivial ergodicity breakdown and strong correlations typically drag the system into out-of-equilibrium states where Boltzmann-Gibbs statistics fails. For a wide class of such systems, it has been shown in recent years that the correct approach is to use Tsallis statistics instead. Here we show how the dynamics of the paradigmatic conservative (area-preserving) stan-dard map exhibits, in an exceptionally clear manner, the crossing from one statistics to the other. Our results unambiguously illustrate the domains of validity of both Boltzmann-Gibbs and Tsallis statistical distributions. Since various important physical systems from particle confinement in magnetic traps to autoionization of molecular Rydberg states, through particle dynamics in accelerators and comet dynamics, can be reduced to the standard map, our results are expected to enlighten and enable an improved interpretation of diverse experimental and observational results.