### 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 |
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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 |

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### Keywords

- Canonical equilibrium distribution
- Helmholtz free energy
- Tsallis entropy

### ASJC Scopus subject areas

- Statistics and Probability
- Condensed Matter Physics

### Cite this

*Physica A: Statistical Mechanics and its Applications*,

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