Why q-Expectation Values Must Be Used In Nonextensive Statistical Mechanics
Author: Abe, Sumiyoshi
Source: Astrophysics and Space Science, Volume 305, Number 3, December 2006 , pp. 241-245(5)
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.
Document Type: Research article
Publication date: 2006-12-01