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This paper brings together four distinct but very important physical notions:1) Entropic force, 2) Entropy-along-a-curve, 3) Tsallis' q-statistics, and 4)Emergent gravitation. We investigate the non additive, classical (Tsallis')q-statistical mechanics of a phase-space curve in $n$ dimensions (3 dimensions,in particular). We focus attention on an entropic force mechanism that yields asimple realization of it, being able to mimic interesting effects such asconfinement, hard core, and asymptotic freedom, typical of high energy physics

Verlinde's emergent gravity in an $\boldsymbol{n-}$dimensional, non-additive Tsallis' scenario