Since energy fluctuations per degree of freedom are only of order 1/ N, the presence of the demon has little effect on macroscopic properties of systems with high numbers of particles. After many iterations of the algorithm, the interplay of demon and random energy changes equilibrates the system. Assuming that a particular system approaches all possible states over very long times (quasi-ergodicity), the resulting Monte Carlo dynamics realistically sample microscopic states that correspond to the given energy value. This is only true if macroscopic quantities are stable over many Monte Carlo steps, i. e. if the system is at equilibrium.