Interaction of a relaxing system with a dynamical environment.

It is shown that nonlinear interactions with a dynamical environment are able to transform the microscopic trajectories of a relaxing system to evolve as a time-dependent multiplicative process. When averaged over an ensemble of such trajectories, a nonexponential response with a scaled relaxation time is generated. Similar features have been observed for dispersive transport and relaxation in experiments and simulations of interacting constituents in condensed matter. This new class of statistical-mechanical systems is illustrated using a Hamiltonian-driven damped Fermi accelerator and an asymmetrically damped stadium billiard