Tsallis power laws and finite baths with negative heat capacity

G. Baris Bagci, Thomas Oikonomou

Research output: Contribution to journalArticle

15 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
Externally publishedYes

Fingerprint

Heat Capacity
baths
Power Law
specific heat
Fat Tails
fats
equipartition theorem
Equipartition
Heat Bath
statistical mechanics
Statistical Mechanics
Central limit theorem
cut-off
Hamiltonian Systems
theorems
degrees of freedom
Correspondence
Degree of freedom
heat
Decay

ASJC Scopus subject areas

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

Cite this

Tsallis power laws and finite baths with negative heat capacity. / Bagci, G. Baris; Oikonomou, Thomas.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 88, No. 4, 042126, 14.10.2013.

Research output: Contribution to journalArticle

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