### Abstract

Plastino and Curado [A. Plastino, E.M.F. Curado, Phys. Rev. E 72 (2005) 047103] recently determined the equilibrium probability distribution for the canonical ensemble using only phenomenological thermodynamical laws as an alternative to the entropy maximization procedure of Jaynes. In the current paper we present another alternative derivation of the canonical equilibrium probability distribution, which is based on the definition of the Helmholtz free energy (and its being constant at the equilibrium) and the assumption of the uniqueness of the equilibrium probability distribution. Noting that this particular derivation is applicable for all trace-form entropies, we also apply it to the Tsallis entropy, showing that the Tsallis entropy yields genuine inverse power laws.

Original language | English |
---|---|

Pages (from-to) | 6386-6389 |

Number of pages | 4 |

Journal | Physica A: Statistical Mechanics and its Applications |

Volume | 391 |

Issue number | 24 |

DOIs | |

Publication status | Published - Dec 15 2012 |

Externally published | Yes |

### Fingerprint

### Keywords

- Canonical equilibrium distribution
- Helmholtz free energy
- Tsallis entropy

### ASJC Scopus subject areas

- Condensed Matter Physics
- Statistics and Probability

### Cite this

*Physica A: Statistical Mechanics and its Applications*,

*391*(24), 6386-6389. https://doi.org/10.1016/j.physa.2012.07.072

**Canonical equilibrium distribution derived from Helmholtz potential.** / Oikonomou, Thomas; Baris Bagci, G.; Tirnakli, Ugur.

Research output: Contribution to journal › Article

*Physica A: Statistical Mechanics and its Applications*, vol. 391, no. 24, pp. 6386-6389. https://doi.org/10.1016/j.physa.2012.07.072

}

TY - JOUR

T1 - Canonical equilibrium distribution derived from Helmholtz potential

AU - Oikonomou, Thomas

AU - Baris Bagci, G.

AU - Tirnakli, Ugur

PY - 2012/12/15

Y1 - 2012/12/15

N2 - Plastino and Curado [A. Plastino, E.M.F. Curado, Phys. Rev. E 72 (2005) 047103] recently determined the equilibrium probability distribution for the canonical ensemble using only phenomenological thermodynamical laws as an alternative to the entropy maximization procedure of Jaynes. In the current paper we present another alternative derivation of the canonical equilibrium probability distribution, which is based on the definition of the Helmholtz free energy (and its being constant at the equilibrium) and the assumption of the uniqueness of the equilibrium probability distribution. Noting that this particular derivation is applicable for all trace-form entropies, we also apply it to the Tsallis entropy, showing that the Tsallis entropy yields genuine inverse power laws.

AB - Plastino and Curado [A. Plastino, E.M.F. Curado, Phys. Rev. E 72 (2005) 047103] recently determined the equilibrium probability distribution for the canonical ensemble using only phenomenological thermodynamical laws as an alternative to the entropy maximization procedure of Jaynes. In the current paper we present another alternative derivation of the canonical equilibrium probability distribution, which is based on the definition of the Helmholtz free energy (and its being constant at the equilibrium) and the assumption of the uniqueness of the equilibrium probability distribution. Noting that this particular derivation is applicable for all trace-form entropies, we also apply it to the Tsallis entropy, showing that the Tsallis entropy yields genuine inverse power laws.

KW - Canonical equilibrium distribution

KW - Helmholtz free energy

KW - Tsallis entropy

UR - http://www.scopus.com/inward/record.url?scp=84865863983&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84865863983&partnerID=8YFLogxK

U2 - 10.1016/j.physa.2012.07.072

DO - 10.1016/j.physa.2012.07.072

M3 - Article

AN - SCOPUS:84865863983

VL - 391

SP - 6386

EP - 6389

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

SN - 0378-4371

IS - 24

ER -