Nonadditive entropy: The Concept and its use
May 20, 2009Citations per year
Abstract: (arXiv)
The entropic form is, for any , {\it nonadditive}. Indeed, for two probabilistically independent subsystems, it satisfies . This form will turn out to be {\it extensive} for an important class of nonlocal correlations, if is set equal to a special value different from unity, noted (where stands for ). In other words, for such systems, we verify that , thus legitimating the use of the classical thermodynamical relations. Standard systems, for which is extensive, obviously correspond to . Quite complex systems exist in the sense that, for them, no value of exists such that is extensive. Such systems are out of the present scope: they might need forms of entropy different from , or perhaps -- more plainly -- they are just not susceptible at all for some sort of thermostatistical approach. Consistently with the results associated with , the -generalizations of the Central Limit Theorem and of its extended L\'evy-Gnedenko form have been achieved. These recent theorems could of course be the cause of the ubiquity of -exponentials, -Gaussians and related mathematical forms in natural, artificial and social systems. All of the above, as well as presently available experimental, observational and computational confirmations -- in high energy physics and elsewhere --, are briefly reviewed. Finally, we address a confusion which is quite common in the literature, namely referring to distinct physical mechanisms {\it versus} distinct regimes of a single physical mechanism.Note:
- Brief review to appear in "Statistical Power-Law Tails in High Energy Phenomena", ed. T.S. Biro, Eur. Phys. J. A (2009);10 pages including 3 figures
- 05.90.+m
- 05.70.-a
- 02.50.Cw
- 05.20.-y
- entropy
- thermodynamics
- statistical mechanics
References(67)
Figures(8)