Fast Hamiltonian chaos: Heat bath without thermodynamic limit.

Chaotic Hamiltonian systems with time scale separation display features known from nonequilibrium statistical physics even when no thermodynamic limit is involved. In particular, fast chaotic degrees of freedom can be modeled by suitable stochastic forces and a Fokker-Planck equation governing the slow parts of the motion can be derived. It turns out that the underlying Hamiltonian structure results in fluctuation-dissipation relations which link the parameters of the effective stochastic model. Such properties are crucial to ensure the correct stationary state of the stochastic description. Our results demonstrate that concepts from thermodynamics can be transferred to dynamical systems with few degrees of freedom.