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