Tsallis power laws and finite baths with negative heat capacity

G. Baris Bagci, Thomas Oikonomou

Research output: Contribution to journalArticlepeer-review

23 Citations (Scopus)

Abstract

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.

Original languageEnglish
Article number042126
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume88
Issue number4
DOIs
Publication statusPublished - Oct 14 2013

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics

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