Modeling fast chaotic degrees of freedom by suitable stochastic processes

Projection operator techniques known from nonequilibrium statistical mechanics are applied to eliminate fast chaotic degrees of freedom in a low-dimensional dynamical system. A perturbative approach shows that the slow degrees of freedom can be modeled by an effective stochastic differential equation.

In the Hamiltonian case a fluctuation-dissipation relation holds which is crucial for respecting the conservation of energy. A comparison of the effective dynamics with the exact one shows the accuracy of the stochastic approximation on all time scales.