Necessity of q-expectation value in nonextensive statistical mechanics

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2005-01-01

Author

Abe, S
Bagci, GB

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In nonextensive statistical mechanics, two kinds of definitions have been considered for expectation value 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 Shore-Johnson theorem for consistent minimum cross-entropy (i.e., relative-entropy) principle is found to select the formalism with the normalized q-expectation value and to exclude the possibility of using the ordinary expectation value from nonextensive statistical mechanics.

Subject Keywords

Maximum-entropy, Tsallis, Law, Principle, Systems, Theorem, Maps, Form

URI

https://hdl.handle.net/11511/65029

Journal

PHYSICAL REVIEW E

DOI

https://doi.org/10.1103/physreve.71.016139

Collections

Department of Physics, Article

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Citation Formats

S. Abe and G. Bagci, “Necessity of q-expectation value in nonextensive statistical mechanics,” PHYSICAL REVIEW E, pp. 0–0, 2005, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/65029.