Equilibrium microstates which generate second law violating steady states

For reversible deterministic N-particle thermostatted systems, we examine the question of why it is so difficult to find initial microstates that will, at long times under the influence of an external dissipative field and a thermostat, lead to second law violating nonequilibrium steady states. We prove that the measure of those phases that generate second law violating phase space trajectories vanishes exponentially with time.