{
  "id": "1608.04052",
  "version": "v1",
  "published": "2016-08-14T02:45:46.000Z",
  "updated": "2016-08-14T02:45:46.000Z",
  "title": "Group theory, entropy and the third law of thermodynamics",
  "authors": [
    "Bilal Canturk",
    "Thomas Oikonomou",
    "G. Baris Bagci"
  ],
  "comment": "8 pages, 2 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "Curado \\textit{et al.} [Ann. Phys. \\textbf{366} (2016) 22] 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 $\\left\\lbrace a,b,r \\right\\rbrace $ 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 $-1 < r < 0$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-08-14T02:45:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "third law",
      "group theory",
      "thermodynamics",
      "distinct universality class",
      "three-parameter entropy expression"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 8,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}