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Statistical and Nonlinear Physics

Maximum entropy principle and power-law tailed distributions

Profile image of Giorgio KaniadakisGiorgio Kaniadakis

2009, The European Physical Journal B

https://doi.org/10.1140/EPJB/E2009-00161-0
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Abstract

In generalized statistical mechanics the second link is customarily relaxed. Of course, the generalized exponential function defining the probability distribution function after inversion, produces a generalized logarithm Λ(pi). But, in general, the mean value of −Λ(pi) is not the entropy of the system. Here we reconsider the question first posed in [Phys. Rev. E 66, 056125 (2002) and 72, 036108 ], if and how is it possible to select generalized statistical theories in which the above mentioned twofold link between entropy and the distribution function continues to hold, such as in the case of ordinary statistical mechanics.

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    Nonlinear Dynamics, 2016

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    Comment on “Quantum Kaniadakis entropy under projective measurement”
    S. Zozor

    Physical Review E, 2016

    We comment on the main result given by Ourabah et al. [Phys. Rev. E 92, 032114 (2015)], noting that it can be derived as a special case of the more general study that we have provided in [Quantum Inf Process 15, 3393 (2016)]. Our proof of the nondecreasing character under projective measurements of so-called generalized (h,φ) entropies (that comprise the Kaniadakis family as a particular case) has been based on majorization and Schur-concavity arguments. As a consequence, we have obtained that this property is obviously satisfied by Kaniadakis entropy but at the same time is fulfilled by all entropies preserving majorization. In addition, we have seen that our result holds for any bistochastic map, being a projective measurement a particular case. We argue here that looking at these facts from the point of view given in [Quantum Inf Process 15, 3393 (2016)] not only simplifies the demonstrations but allows for a deeper understanding of the entropic properties involved.

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    Entropy Analysis of a Railway Network’s Complexity
    Antonio Lopes

    Entropy, 2016

    Railway networks are among the many physical systems that reveal a fractal structure. This paper studies the Portuguese railway system, and analyzes how it evolved over time, namely what concerns the structure of its different levels, and its distribution over the territory. Different mathematical tools are adopted, such as fractal dimension, entropy and state space portrait. The results are consistent with the historical evolution of the network.

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