Why q-Expectation Values Must Be Used In Nonextensive Statistical Mechanics

Details Why q-Expectation Values Must Be Used In Nonextensive Statistical Mechanics Why q-Expectation Values Must Be Used In Nonextensive Statistical Mechanics

Dec 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006ap%26ss.305..241a&link_type=abstract

Astrophysics and Space Science, Volume 305, Issue 3, pp.241-245

Astronomy and Astrophysics

Astrophysics

10

Scientific paper

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.

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