q-Calculus Framework For Entropy In Multifractal Distributions

Details q-Calculus Framework For Entropy In Multifractal Distributions q-Calculus Framework For Entropy In Multifractal Distributions

1998-03-02

arxiv.org/abs/cond-mat/9803017v1

Physics

Condensed Matter

Statistical Mechanics

Latex, pages 8, one latex figure, e-mail: raman%phys@puniv.chd.nic.in

Scientific paper

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.

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