2004/04/11 by Sumiyoshi Abe, Abe, Sumiyoshi, G. B. Bagci +2
Physics and Astronomy · #Advanced Mathematical Theories and Applications #Advanced Thermodynamics and Statistical Mechanics #FOS: Physical sciences #Other Condensed Matter (cond-mat.other) #Statistical Mechanics (cond-mat.stat-mech) #Statistical Mechanics and Entropy #cond-mat.other #cond-mat.stat-mech
paper · pdf · doi:10.48550/arxiv.cond-mat/0404253
17 pages, no figures
arxiv created 2004/04/11 · openalex publication_date 2004/04/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In nonextensive statistical mechanics, two kinds of definitions have been considered for expectation valu of a physical quantity: one is the ordinary definition and the other is the normalized q-expectation value employing the escort distribution. Since both of them lead to the maximum-Tsallis-entropy distributions of a similar type, it is of crucial importance to determine which the correct physical one is. A point is that the definition of expectation value is indivisibly connected to the form of generalized relative entropy. Studying the properties of the relative entropies associated with these two definitions, it is shown how the use of the escort distribution is essential. In particular, the axiomatic framework proposed by Shore and Johnson is found to support the formalism with the normalized q-expectation value and to exclude the ordinary expectation value in nonextensive statistical mechanics.