  We present aspects of the moduli of curve families on a metric measure space
which may prove useful in calculating, or in providing bounds to, non-additive
entropies having a power-law functional form. We use as paradigmatic cases the
calculations of the moduli of curve families for a cylinder and for an annulus
in $\mathbb{R}^n$. The underlying motivation for these studies is that the
definitions and some properties of the modulus of a curve family resembles
those of the Tsallis entropy, when the latter is seen from a micro-canonical
viewpoint. We comment on the origin of the conjectured invariance of the
Tsallis entropy under M\"obius transformations of the non-extensive (entropic)
parameter. Needing techniques applicable to both locallly Euclidean and fractal
classes of spaces, we examine the behavior of the Tsallis functional, via the
modulus, under quasi-conformal maps. We comment on properties of such maps and
their possible significance for the dynamical foundations of power-law
entropies.
