Author: Abe, Sumiyoshi

Source: Astrophysics and Space Science, Volume 305, Number 3, December 2006 , pp. 241-245(5)

Publisher: Springer

Abstract:

There is a controversy in the area of nonextensive statistical mechanics regarding the form of the expectation value of a physical quantity. Two definitions have been discussed in the literature: one is the ordinary definition and the other is the normalized q-expectation value associated with the escort distribution. Here, it is proved that the normalized q-expectation value is the correct one to be employed. The Shore-Johnson theorem is used to show that the formalism with the normalized q-expectation value is theoretically consistent with minimum cross entropy principle, whereas the ordinary expectation value has to be excluded.

Keywords: q-expectation values; nonextensive statistical mechanics

Document Type: Research article

DOI: http://dx.doi.org/10.1007/s10509-006-9198-5

Affiliations: 1: Email: suabe@sf6.so-net.ne.jp

Publication date: 2006-12-01

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