Lorenz deterministic diffusion
  The Lorenz 1963 dynamical system is known to reduce in the steady state to a one-dimensional motion of a classical particle subjected to viscous damping in a past history-dependent potential field. If the potential field is substituted by a periodic function of the position, the resulting system shows a rich dynamics where (standard) diffusive behaviours, ballistc motions and trapping take place by varying the model control parameters. This system permits to highlight the intimate relation between chaos and long-time deterministic diffusion. 
R. Festa, A. Mazzino, and D. Vincenzi