Why q-Expectation Values Must Be Used In Nonextensive Statistical Mechanics |
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| Authors: | Sumiyoshi Abe |
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| Institution: | (1) Institute of Physics, University of Tsukuba, Ibaraki 305-8571, Japan |
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| 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. |
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| Keywords: | q-expectation values nonextensive statistical mechanics |
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