On the Duality of q-Logarithmic Decay Constants and the Two Forms of the Eastmond Non-Extensive Decay Modulator

We show that the Tsallis q-logarithm admits two distinct decay constant formula- tions, related by the symmetry lnq(1/x) =−ln2−q(x). The Eastmond Non-Extensive Decay Modulator (NEDM) therefore exists in two dual forms: a half-life definition EHL(q) =−lnq(1/2)/ln 2, and an operational definition Eop(q) = lnq(2)/ln 2. These are not identical but are mirror images under the dual map q →2−q. We derive the symmetry law, establish the properties of both modulators, and discuss the physical cir- cumstances under which each definition is appropriate. Failure to distinguish between the two forms leads to a reversal of the predicted deviation from classical exponential decay.