Generalization of multifractal theory within quantum calculus
Abstract
On the basis of the deformed series in quantum calculus, we generalize the partition function and the mass exponent of a multifractal, as well as the average of a random variable distributed over a selfsimilar set. For the partition function, such expansion is shown to be determined by binomialtype combinations of the Tsallis entropies related to manifold deformations, while the mass exponent expansion generalizes the known relation τ_{q}=D_{q}(q1). We find the equation for the set of averages related to ordinary, escort, and generalized probabilities in terms of the deformed expansion as well. Multifractals related to the Cantor binomial set, exchange currency series, and poroussurface condensates are considered as examples.
 Publication:

EPL (Europhysics Letters)
 Pub Date:
 March 2010
 DOI:
 10.1209/02955075/89/50007
 arXiv:
 arXiv:1003.0124
 Bibcode:
 2010EL.....8950007O
 Keywords:

 Condensed Matter  Statistical Mechanics
 EPrint:
 12 pages, 4 figures, accepted by EPL