q-Calculus Framework For Entropy In Multifractal Distributions
نویسنده
چکیده
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. Non-extensive Tsallis Thermostatistics ( NTT) [1] generalizes the BoltzmannGibbs (BG) statistics, to treat the non-extensivity of physical systems [2]. It has been applied with success to many different situations (for complete reviews, see ref. [3]). One non-extensive quantity which is playing a useful role is Tsallis entropy [4]. Given a probability distribution {pi}i=1,...,W where i is the index for system configuration, Tsallis entropy is given by S q = 1− ∑W i=1(pi) q q − 1 . (1) ∗Postal Address: 1110, 36-C, Chandigarh -160014, India
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