### Abstract

Curado etï¿½al. (2016) have recently studied the axiomatic structure and the universality of a three-parameter trace-form entropy inspired by the group-theoretical structure. In this work, we study the group-theoretical entropy S_{a,b,r} in the context of the third law of thermodynamics where the parameters {a,b,r} are all independent. We show that this three-parameter entropy expression can simultaneously satisfy the third law of thermodynamics and the three Khinchin axioms, namely continuity, concavity and expansibility only when the parameter b is set to zero. In other words, it is thermodynamically valid only as a two-parameter generalization S_{a,r}. Moreover, the restriction set by the third law i.e., the condition b=0, is important in the sense that the so obtained two-parameter group-theoretical entropy becomes extensive only when this condition is met. We also illustrate the interval of validity of the third law using the one-dimensional Ising model with no external field. Finally, we show that the S_{a,r} is in the same universality class as that of the Kaniadakis entropy for 0<r<1 while it has a distinct universality class in the interval −1<r<0.

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

Pages (from-to) | 62-70 |

Number of pages | 9 |

Journal | Annals of Physics |

Volume | 377 |

DOIs | |

Publication status | Published - Feb 1 2017 |

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### Keywords

- Extensivity
- Generalized entropies
- Group theory
- Khinchin axioms
- Third law of thermodynamics

### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Annals of Physics*,

*377*, 62-70. https://doi.org/10.1016/j.aop.2016.12.013

**Group theory, entropy and the third law of thermodynamics.** / Canturk, Bilal; Oikonomou, Thomas; Bagci, G. Baris.

Research output: Contribution to journal › Article

*Annals of Physics*, vol. 377, pp. 62-70. https://doi.org/10.1016/j.aop.2016.12.013

}

TY - JOUR

T1 - Group theory, entropy and the third law of thermodynamics

AU - Canturk, Bilal

AU - Oikonomou, Thomas

AU - Bagci, G. Baris

PY - 2017/2/1

Y1 - 2017/2/1

N2 - Curado etï¿½al. (2016) have recently studied the axiomatic structure and the universality of a three-parameter trace-form entropy inspired by the group-theoretical structure. In this work, we study the group-theoretical entropy Sa,b,r in the context of the third law of thermodynamics where the parameters {a,b,r} are all independent. We show that this three-parameter entropy expression can simultaneously satisfy the third law of thermodynamics and the three Khinchin axioms, namely continuity, concavity and expansibility only when the parameter b is set to zero. In other words, it is thermodynamically valid only as a two-parameter generalization Sa,r. Moreover, the restriction set by the third law i.e., the condition b=0, is important in the sense that the so obtained two-parameter group-theoretical entropy becomes extensive only when this condition is met. We also illustrate the interval of validity of the third law using the one-dimensional Ising model with no external field. Finally, we show that the Sa,r is in the same universality class as that of the Kaniadakis entropy for 0

AB - Curado etï¿½al. (2016) have recently studied the axiomatic structure and the universality of a three-parameter trace-form entropy inspired by the group-theoretical structure. In this work, we study the group-theoretical entropy Sa,b,r in the context of the third law of thermodynamics where the parameters {a,b,r} are all independent. We show that this three-parameter entropy expression can simultaneously satisfy the third law of thermodynamics and the three Khinchin axioms, namely continuity, concavity and expansibility only when the parameter b is set to zero. In other words, it is thermodynamically valid only as a two-parameter generalization Sa,r. Moreover, the restriction set by the third law i.e., the condition b=0, is important in the sense that the so obtained two-parameter group-theoretical entropy becomes extensive only when this condition is met. We also illustrate the interval of validity of the third law using the one-dimensional Ising model with no external field. Finally, we show that the Sa,r is in the same universality class as that of the Kaniadakis entropy for 0

KW - Extensivity

KW - Generalized entropies

KW - Group theory

KW - Khinchin axioms

KW - Third law of thermodynamics

UR - http://www.scopus.com/inward/record.url?scp=85009290696&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85009290696&partnerID=8YFLogxK

U2 - 10.1016/j.aop.2016.12.013

DO - 10.1016/j.aop.2016.12.013

M3 - Article

VL - 377

SP - 62

EP - 70

JO - Annals of Physics

JF - Annals of Physics

SN - 0003-4916

ER -