### Abstract

It is well-known that the partition function can consistently be factorized from the canonical equilibrium distribution obtained through the maximization of the Shannon entropy. We show that such a normalized and factorized equilibrium distribution is warranted if and only if the entropy measure I{(p)} has an additive slope i.e. ∂I{(p)}/∂p_{i} when the ordinary linear averaging scheme is used. Therefore, we conclude that the maximum entropy principle of Jaynes should not be used for the justification of the partition functions and the concomitant thermodynamic observables for generalized entropies with non-additive slope subject to linear constraints. Finally, Tsallis and Rï¿½nyi entropies are shown not to yield such factorized canonical-like distributions.

Original language | English |
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Pages (from-to) | 207-211 |

Number of pages | 5 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 381 |

Issue number | 4 |

DOIs | |

Publication status | Published - Jan 30 2017 |

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### Keywords

- Entropy maximization
- Factorized canonical distributions
- Partition function
- Tsallis/Rï¿½nyi entropy

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

**Misusing the entropy maximization in the jungle of generalized entropies.** / Oikonomou, Thomas; Bagci, G. Baris.

Research output: Contribution to journal › Article

*Physics Letters, Section A: General, Atomic and Solid State Physics*, vol. 381, no. 4, pp. 207-211. https://doi.org/10.1016/j.physleta.2016.11.005

}

TY - JOUR

T1 - Misusing the entropy maximization in the jungle of generalized entropies

AU - Oikonomou, Thomas

AU - Bagci, G. Baris

PY - 2017/1/30

Y1 - 2017/1/30

N2 - It is well-known that the partition function can consistently be factorized from the canonical equilibrium distribution obtained through the maximization of the Shannon entropy. We show that such a normalized and factorized equilibrium distribution is warranted if and only if the entropy measure I{(p)} has an additive slope i.e. ∂I{(p)}/∂pi when the ordinary linear averaging scheme is used. Therefore, we conclude that the maximum entropy principle of Jaynes should not be used for the justification of the partition functions and the concomitant thermodynamic observables for generalized entropies with non-additive slope subject to linear constraints. Finally, Tsallis and Rï¿½nyi entropies are shown not to yield such factorized canonical-like distributions.

AB - It is well-known that the partition function can consistently be factorized from the canonical equilibrium distribution obtained through the maximization of the Shannon entropy. We show that such a normalized and factorized equilibrium distribution is warranted if and only if the entropy measure I{(p)} has an additive slope i.e. ∂I{(p)}/∂pi when the ordinary linear averaging scheme is used. Therefore, we conclude that the maximum entropy principle of Jaynes should not be used for the justification of the partition functions and the concomitant thermodynamic observables for generalized entropies with non-additive slope subject to linear constraints. Finally, Tsallis and Rï¿½nyi entropies are shown not to yield such factorized canonical-like distributions.

KW - Entropy maximization

KW - Factorized canonical distributions

KW - Partition function

KW - Tsallis/Rï¿½nyi entropy

UR - http://www.scopus.com/inward/record.url?scp=85006128027&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85006128027&partnerID=8YFLogxK

U2 - 10.1016/j.physleta.2016.11.005

DO - 10.1016/j.physleta.2016.11.005

M3 - Article

AN - SCOPUS:85006128027

VL - 381

SP - 207

EP - 211

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 4

ER -