On time's arrow in Ehrenfest models with reversible deterministic dynamics

We introduce a deterministic, time-reversible version of the Ehrenfest urn model. The distribution of first-passage times from equilibrium to non-equi librium states and vice versa is calculated. We find that average times for transition to non-equilibrium always scale exponentially with the system s ize, whereas the timescale for relaxation to equilibrium depends on microsc opic dynamics. To illustrate this, we also look at deterministic and stocha stic versions of the Ehrenfest model with a distribution of microscopic rel axation times.