Deformed logarithms and entropies

Details Deformed logarithms and entropies Deformed logarithms and entropies

2004-02-16

arxiv.org/abs/cond-mat/0402418v1

Physica A340:41-49,2004

Physics

Condensed Matter

Statistical Mechanics

Presented at next2003, Second Sardinian International Conference on News and Expectations in Thermostatistics, Villasimius (Ca

Scientific paper

10.1016/j.physa.2004.03.075

By solving a differential-functional equation inposed by the MaxEnt principle we obtain a class of two-parameter deformed logarithms and construct the corresponding two-parameter generalized trace-form entropies. Generalized distributions follow from these generalized entropies in the same fashion as the Gaussian distribution follows from the Shannon entropy, which is a special limiting case of the family. We determine the region of parameters where the deformed logarithm conserves the most important properties of the logarithm, and show that important existing generalizations of the entropy are included as special cases in this two-parameter class.

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