An equilibrium thermostatistics of a nonextensive finite system: Canonical distribution and entropy

Jian, Jiang; Wang, R.; Lysogorskii, Yuri V.; Zvezdov, D.; Tayurskiı̆, D. A.; Wang, Q.A.

doi:10.1016/j.physa.2012.01.012

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“…However, if this is done, the probability distribution is found to be neither exponential nor q exponential [26] [see Eq. (18) therein].…”

Section: Discussionmentioning

confidence: 99%

Tsallis power laws and finite baths with negative heat capacity

Bagci

Oikonomou

2013

Phys. Rev. E

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It is often stated that heat baths with finite degrees of freedom i.e., finite baths, are sources of Tsallis distributions for classical Hamiltonian systems. By using well-known fundamental statistical mechanics expressions, we rigorously show that Tsallis distributions with fat tails are possible only for finite baths with constant negative heat capacity, while constant positive heat capacity finite baths yield decays with sharp cutoff with no fat tails. However, the correspondence between Tsallis distributions and finite baths holds at the expense of violating the equipartition theorem for finite classical systems at equilibrium. We comment on the implications of the finite bath for the recent attempts towards a q-generalized central limit theorem.

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“…However, if this is done, the probability distribution is found to be neither exponential nor q exponential [26] [see Eq. (18) therein].…”

Section: Discussionmentioning

confidence: 99%