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 a simple realization of it, being able to mimic interesting effects such as confinement, hard core, and asymptotic freedom, typical of high energy physics.