Finite-precision stationary states at and away from equilibrium

We study the precision dependence of equilibrium and nonequilibrium phase-space distribution functions for time-reversible dynamical systems simulated with finite, computational precision. The conservative and dissipative cases show different behavior, with substantially reduced period lengths in the dissipative case. The main effect of finite precision is to change the phase-space fraction occupied by the distributions. The convergence of thermodynamic averages is only slightly affected. We introduce and discuss a simple stochastic model which is nicely consistent with all of our numerical results. This model links the length of periodic orbits to the strange attractor's correlation dimension.