Nonextensive statistical mechanics: A brief introduction

• Published in: Continuum mechanics and thermodynamics Vol. 16; no. 3; pp. 223 - 235
• Main Authors: Tsallis, C., Brigatti, E.
• Format: Journal Article
• Language: English
• Published: Heidelberg Springer Nature B.V 01-03-2004
• Subjects: Entropy; Statistical mechanics; Thermodynamics
• ISSN: 0935-1175; 1432-0959
• DOI: 10.1007/s00161-004-0174-4

Boltzmann-Gibbs statistical mechanics is based on a specific entropy. 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 (with , and ). 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. [PUBLICATION ABSTRACT]