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Title: Group theory, entropy and the third law of thermodynamics
Authors: Cantürk, Bilal
Oikonomou, Thomas
Bağcı, Gökhan Barış
Keywords: Generalized entropies
Group theory
Third law of thermodynamics
Khinchin axioms
Issue Date: 2017
Publisher: Academic Press Inc Elsevier Science
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 S-a,S-b,S-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,S-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,S-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. (C) 2016 Elsevier Inc. All rights reserved.
ISSN: 0003-4916
Appears in Collections:Malzeme Bilimi ve Nanoteknoloji Mühendisliği Bölümü / Department of Material Science & Nanotechnology Engineering
Scopus İndeksli Yayınlar Koleksiyonu / Scopus Indexed Publications Collection
WoS İndeksli Yayınlar Koleksiyonu / WoS Indexed Publications Collection

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