Abstract
Curado et�al. (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<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
Group theory, entropy and the third law of thermodynamics. / Canturk, Bilal; Oikonomou, Thomas; Bagci, G. Baris.
In: Annals of Physics, Vol. 377, 01.02.2017, p. 62-70.Research output: Contribution to journal › Article
}
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 et�al. (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 et�al. (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 -