  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.
