Nonextensive Entropy, Prior PDFs and Spontaneous Symmetry Breaking

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Shafee, Fariel;
(2008)
  • Subject: Physics - Data Analysis, Statistics and Probability | Nonlinear Sciences - Adaptation and Self-Organizing Systems | Condensed Matter - Statistical Mechanics
    arxiv: Computer Science::Databases

We show that using nonextensive entropy can lead to spontaneous symmetry breaking when a parameter changes its value from that applicable for a symmetric domain, as in field theory. We give the physical reasons and also show that even for symmetric Dirichlet priors, suc... View more
  • References (9)

    [1] C. Tsallis, Possible generalization of Boltzmann-Gibbs statistics, J. Stat.Phys. 52, 479-487 (1988).

    [2] F. Shafee, Lambert function and a new non-extensive form of entropy, IMA Journal of Applied Mathematics 72, 785-800 (2007)

    [3] G. Kaniadakis, Nonlinear kinetics underlying generalized statistics. Physica A 296, 405-425 (2001).

    [4] G. Kaniadakis, Statistical mechanics in the context of special relativity. Phys. Rev. E 66, 056125 (2002).

    [5] I. Nemenman, F. Shafee and W. Bialek, Entropy and Inference, Revisited, in Adv. Neur. Info. Processing 14, eds. T.G. Dietterich, S. Becker and Z. Ghahramani (MIT Press, Cambridge, 2002) pp. 471-478.

    [6] F. Shafee, Generalized Entropy with Clustering and Quantum Entangled States. cond-mat/0410554 (accepted by Chaos, Solitons and Fractals)(2008)

    [7] W. Bialek, C.G. Callan and S.P. Strong, Field theories for learning probability distributions.Phys. Rev. Lett. 77, 4693-4697 (1996)

    [8] D. Wolpert and D. Wolf, Estimating functions of probability distributions from a finite set of samples, Phys. Rev. E, 52, 6841-6854 (1995).

    [9] E.T. Jaynes, Monkeys, Kangaroos, and N, University of Cambridge Physics Dept. Report 1189 (1984).

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