2004/11/03 by Yuzuru Sato, Constantino Tsallis, Sato, Yuzuru +1
Economics, Econometrics and Finance · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #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/0411073
10 pages including 7 figures. Invited paper to appear in a special issue of the International Journal of Bifurcation and Chaos: Proceedings of the Summer School and Conference on Complexity at Patras and Olympia (July 2004), Ed. T. Bountis
arxiv created 2004/11/03 · openalex publication_date 2004/11/03 · arxiv updated 2009/12/01 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28
Many natural and artificial systems whose range of interaction is long enough are known to exhibit (quasi)stationary states that defy the standard, Boltzmann-Gibbs statistical mechanical prescriptions. For handling such anomalous systems (or at least some classes of them), \it nonextensive statistical mechanics has been proposed based on the entropy Sq≡ k (1-∑i=1Wpiq)/(q-1), with S1=-kΣi=1W pi ln pi (Boltzmann-Gibbs entropy). Special collective correlations can be mathematically constructed such that the strictly \it additive entropy is now Sq for an adequate value of q ≠ 1, whereas Boltzmann-Gibbs entropy is \it nonadditive. Since important classes of systems exist for which the strict additivity of Boltzmann-Gibbs entropy is replaced by asymptotic additivity (i.e., extensivity), a variety of classes are expected to exist for which the strict additivity of Sq (q≠ 1) is similarly replaced by asymptotic additivity (i.e., extensivity). All probabilistically well defined systems whose adequate entropy is S1 are called \it extensive (or \it normal). They correspond to a number W\it eff of \it effectively occupied states which grows \it exponentially with the number N of elements (or subsystems). Those whose adequate entropy is Sq (q ≠ 1) are currently called \it nonextensive (or \it anomalous). They correspond to W\it eff growing like a \it power of N. To illustrate this scenario, recently addressed, we provide in this paper details about systems composed by N=2,3 two-state subsystems.