“…When B = 0 and A is a gradient of a potential A = ∇V , (3) is called a generalised Langevin dynamic in [12,15]. In this case, (3) belongs to the class of weakly interacting particle systems and have been used widely in applied sciences, especially in plasma physics, see e.g., [8,9,14,10] and references therein. In these papers (3) is considered as a stochastic perturbation, via the external heat bath variable Z t , of the classical deterministic Hamiltonian system for (Q t , P t ).…”