### 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 language | English |
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Article number | 042126 |

Journal | Physical Review E - Statistical, Nonlinear, and Soft Matter Physics |

Volume | 88 |

Issue number | 4 |

DOIs | |

Publication status | Published - Oct 14 2013 |

Externally published | Yes |

### Fingerprint

### 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.

Research output: Contribution to journal › Article

*Physical Review E - Statistical, Nonlinear, and Soft Matter Physics*, vol. 88, no. 4, 042126. https://doi.org/10.1103/PhysRevE.88.042126

}

TY - JOUR

T1 - Tsallis power laws and finite baths with negative heat capacity

AU - Bagci, G. Baris

AU - Oikonomou, Thomas

PY - 2013/10/14

Y1 - 2013/10/14

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84886012660&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84886012660&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.88.042126

DO - 10.1103/PhysRevE.88.042126

M3 - Article

VL - 88

JO - Physical review. E

JF - Physical review. E

SN - 2470-0045

IS - 4

M1 - 042126

ER -