  We test the applicability of the Gallavotti-Cohen fluctuation formula on a
nonequilibrium version of the periodic Ehrenfest wind-tree model. This is a
one-particle system whose dynamics is rather complex (e.g. it appears to be
diffusive at equilibrium), but its Lyapunov exponents are nonpositive. For
small applied field, the system exhibits a very long transient, during which
the dynamics is roughly chaotic, followed by asymptotic collapse on a periodic
orbit. During the transient, the dynamics is diffusive, and the fluctuations of
the current are found to be in agreement with the fluctuation formula, despite
the lack of real hyperbolicity. These results also constitute an example which
manifests the difference between the fluctuation formula and the Evans-Searles
identity.
