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Toward a relative qq-entropy

May 5, 2019
23 pages
Published in:
  • Physica A 545 (2020) 123270
  • Published: May 1, 2020
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Abstract: (Elsevier)
We address the question and related controversy of the formulation of the q -entropy, and its relative entropy counterpart, for models described by continuous (non-discrete) sets of variables. We notice that an Lp normalized functional proposed by Lutwak–Yang–Zhang (LYZ), which is essentially a variation of a properly normalized relative Rényi entropy up to a logarithm, has extremal properties that make it an attractive candidate which can be used to construct such a relative q -entropy. We comment on the extremizing probability distributions of this LYZ functional, its relation to the escort distributions, a generalized Fisher information and the corresponding Cramér–Rao inequality. We point out potential physical implications of the LYZ entropic functional and of its extremal distributions.
Note:
  • Minor changes in this version. 23 pages. No figures. LaTeX2e. To be published in Physica A
  • q -entropy
  • Tsallis entropy
  • Nonadditive entropy
  • Nonextensive thermostatistics
  • Complexity
  • [formula omitted]-entropy
  • entropy
  • information theory
  • [2]

    Introduction to Nonextensive Statistical Mechanics: Approaching a Complex World

    • C. Tsallis
  • [3]
    Encycl.Math.Appl.,vol.115
    • L. Barreira
      ,
    • Y. Pesin
  • [4]
    Encycl.Math.Appl.,vol.54
    • A. Katok
      ,
    • B. Hasselblatt
  • [5]

    Essential discreteness in generalized thermostatistics with non-logarithmic entropy

    • S. Abe
      • EPL 90 (2010) 50004
  • [6]

    Comment on Essential discreteness in generalized thermostatistics with non-logarithmic entropy by Abe Sumiyoshi

    • B.B. Andresen
      • EPL 92 (2010) 40005
  • [7]

    Reply to the comment by B. Andresen

    • S. Abe
      • EPL 92 (2010) 40006
  • [8]
    Comment on Essential discreteness in generalized thermostatistics with non-logarithmic entropy by S. Abe
    • G.B. Bagci
      ,
    • T. Oikonomou
      ,
    • U. Tirnakli
  • [9]

    Nonextensive formalism and continuous Hamiltonian systems

    • J.P. Boon
      ,
    • J.F. Lutsko
      • Phys.Lett.A 375 (2011) 329
  • [10]

    Questioning the validity of non-extensive thermodynamics for classical Hamiltonian systems

    • J.F. Lutsko
      ,
    • J.P. Boon
      • EPL 95 (2011) 20006
  • [11]

    On the putative essential discreteness of q-generalized entropies

    • A. Plastino
      ,
    • M.C. Rocca
      • Physica A 488 (2017) 56
  • [13]

    Comment on Route from discretness to the continuum for the Tsallis q-entropy

    • C. Ou
      ,
    • S. Abe
      • Phys.Rev.E 97 (2018) 066101
  • [14]

    Reply to the comment on Route from discreteness to the continuum for the Tsallis q-entropy by Conjie Ou and Sumiyoshi Abe

    • T. Oikonomou
      ,
    • G.B. Bagci
      • Phys.Rev.E 97 (2018) 066102
  • [16]

    Cramér-Rao and moment-entropy inequalities for Renyi entropy and generalized Fisher information

    • E. Lutwak
      ,
    • D. Yang
      ,
    • G. Zhang
      • IEEE Trans.Info.Theor. 51 (2005) 473
  • [17]

    Dual mixed volumes

    • E. Lutwak
      • Pacific J.Math. 58 (1975) 531
  • [18]

    Intersection bodies and dual mixed volumes

    • E. Lutwak
      • Adv.Math. 71 (1988) 232
  • [19]

    The Brunn–Minkowski-Firey theory I: Mixed volumes and the Minkowski problem

    • E. Lutwak
      • J.Diff.Geom. 38 (1993) 131
  • [20]

    The Brunn–Minkowski-Firey theory II: Affine and geominimal surface areas

    • E. Lutwak
      • Adv.Math. 118 (1996) 244
  • [21]

    Lp affine isoperimetric inequalities

    • E. Lutwak
      ,
    • D. Yang
      ,
    • G. Zhang
      • J.Diff.Geom. 56 (2000) 111
  • [22]

    Sharp affine Lp Sobolev inequalities

    • E. Lutwak
      ,
    • D. Yang
      ,
    • G. Zhang
      • J.Diff.Geom. 62 (2002) 17
  • [23]

    The Cramer-Rao inequality for star bodies

    • E. Lutwak
      ,
    • D. Yang
      ,
    • G. Zhang
      • Duke Math.J. 112 (2002) 59
  • [24]

    Volume inequalities for subspaces of Lp

    • E. Lutwak
      ,
    • D. Yang
      ,
    • G. Zhang
      • J.Diff.Geom. 68 (2004) 159
  • [25]

    Geometric measures in the dual Brunn–Minkowski theory and their associated Minkowski problems

    • Y. Huang
      ,
    • E. Lutwak
      ,
    • D. Yang
      ,
    • G. Zhang
      • Acta Math. 216 (2016) 325
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