Molecular dynamics and time reversibility

We present a time-symmetrical integer arithmetic algorithm for numerical (molecular dynamics) simulations of classical fluids. This algorithm is used to illustrate, through concrete examples, that time-asymmetric evolutions are typical for systems of many particles evolving according to reversible microscopic dynamics and to calculate the asymptotic behavior of the velocity autocorrelation function with an improved accuracy. The equivalence between equilibrium time averages and microcanonical ensemble averages is checked via two new sampling methods for computing microcanonical averages of classical systems.