Generalized entropy optimized by a given arbitrary distribution
Abstract
An ultimate generalization of the maximum entropy principle is presented. An entropic measure, which is optimized by a given arbitrary distribution with the finite linear expectation value of a physical random quantity of interest, is constructed. It is concave irrespective of the properties of the distribution and satisfies the H-theorem for the master equation combined with the principle of microscopic reversibility. This offers a unified basis for a great variety of distributions observed in nature. As examples, the entropies associated with the stretched exponential distribution postulated by Anteneodo and Plastino (1999 J. Phys. A: Math. Gen. 32 1089) and the kappa-deformed exponential distribution by Kaniadaki (2002 Phys. Rev. E 66 056125) and Naudts (2002 Physica A 316 323) are derived. To include distributions with divergent moments (e.g., the Lévy stable distributions), it is necessary to modify the definition of the expectation value.
- Publication:
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Journal of Physics A Mathematical General
- Pub Date:
- August 2003
- DOI:
- 10.1088/0305-4470/36/33/301
- arXiv:
- arXiv:cond-mat/0211437
- Bibcode:
- 2003JPhA...36.8733A
- Keywords:
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- Condensed Matter - Statistical Mechanics
- E-Print:
- 10 pages, no figures