EQUILIBRIUM MICROSTATES WHICH GENERATE 2ND LAW VIOLATING STEADY-STATES

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