q-Calculus Framework For Entropy In Multifractal Distributions

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The connection between Tsallis entropy for a multifractal distribution and Jackson's $q$-derivative is established. Based on this derivation and definition of a homogeneous function, a $q$-analogue of Shannon's entropy is discussed. $q$-additivity of this entropy is shown. We also define $q$-analogue of Kullback relative entropy. The implications of lattice structure beneath $q$-calculus are highlighted in the context of $q$-entropy.
Latex, pages 8, one latex figure, e-mail: raman%phys@puniv.chd.nic.in

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Statistical Mechanics

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http://salesiana.dossiersoluciones.com/handle/123456789/28125

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/cond-mat/9803017
 http://arxiv.org/abs/cond-mat/9803017

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arXiv