Nonextensive statistical mechanics: A brief introduction
By Constantino Tsallis, E. Brigatti. 2003
153 citations recorded by the source corpus.
Abstract.Boltzmann-Gibbs statistical mechanics is based on the entropy $S_{\rm BG} = -k \sum_{i = 1}^W p_i \ln p_i$. It enables a successful thermal approach to ubiquitous systems, such as those involving short-range interactions, markovian processes, and, generally speaking, those systems whose dynamical occupancy of phase space tends to be ergodic. For systems whose microscopic dynamics is more complex, it is natural to expect that the dynamical occupancy of phase space will have a less trivial structure, for example a (multi)fractal or hierarchical geometry. The question naturally arises whether it is possible to study such systems with concepts and methods similar to those of standard statistical mechanics. The answer appears to be yes for ubiquitous systems, but the concept of entropy needs to be adequately generalized. Some classes of such systems can be satisfactorily approached with the entropy $S_q = k\frac{1-\sum_{i = 1}^W p_i^q}{q-1}$ (with $q \in \cal R$, and $S_1 = S_{\rm BG}$). This theory is sometimes referred in the literature as nonextensive statistical mechanics. We provide here a brief introduction to the formalism, its dynamical foundations, and some illustrative applications. In addition to these, we illustrate with a few examples the concept of stability (or experimental robustness) introduced by B. Lesche in 1982 and recently revisited by S. Abe.
Subfields: Condensed Matter Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/34745072cfca90b21a812210903d9c8a8927c545
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In Condensed Matter Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Partitioning diversity into independent alpha and beta components. (2007, methodology): “This is a well-known equation in information theory (Aczel and Daroczy 1975) and physics (Tsallis and Brigatti 2004, Keylock 2005).”
- GST and its relatives do not measure differentiation (2008, methodology): “(eqn 9) This formula has been derived by other means in information theory (Aczel & Daroczy 1975) and physics (Tsallis & Brigatti 2004).”
- Generative Models of Cortical Oscillations: Neurobiological Implications of the Kuramoto Model (2010, unknown): “Its characterization requires novel tools from nonextensive thermodynamics like generalized entropies (Tsallis and Brigatti, 2004; Tsallis, 2006).”