In this thesis, Boltzmann's H-theorem is studied and applied to prove a general convergence to equilibrium for the adiabatic piston paradox, governed by a specially-derived kinetic Fokker-Planck equation. We review general results in kinetic theory on the Boltzmann collision operator, and rates of convergence to equilibrium. Furthermore, we turn our attention to simulations of the piston paradox, and apply the algorithm of Sigureirsson et al. for particle-particle collision dynamics to the piston setting, determining empirically the optimal parameters.