Duality and spatial inhomogeneity

Within the framework on non-extensive thermostatistics we revisit the recently advanced q-duality concept. We focus our attention here on a modified q-entropic measure of the spatial inhomogeneity for binary patterns. At a fixed length scale this measure exhibits a generalised duality that links appropriate pairs of q and q′ values. The simplest q↔q′ invariant function, without any free parameters, is deduced here. Within an adequate interval q<q0<q′, in which the function reaches its maximum value at q0, this invariant function accurately approximates the investigated q-measure, nitidly evidencing the duality phenomenon. In the close vicinity of q0, the approximate meaningful relation q+q′≅2q0 holds.