q calculus and entropy in nonextensive statistical physics

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 analog of Shannon's entropy is defined. Tsallis entropy can also be accommodated in this formalism. Pseudoadditivity of the q entropies is proved. We also define a q analog of Kullback relative entropy. The implications of the lattice structure beneath the q calculus are highlighted in the context of the q entropy. [S1063-651X(98)08809-6].