Order from disorder in closed systems via time reversal violation

Definitions of entropy usually assume time-reversal (T) invariance of interactions, yet microscopically T is known to be violated. We present a detailed computational example of (uncharged) particle species separation (Maxwell demon) using an interaction that violates both parity (P) and T so that PT is preserved, consistent with the CPT invariance required in quantum field theory (C is charge conjugation). This illustrates how T-violating forces can produce more organized states from disorganized ones, contrary to expectations based on increase of entropy. We also outline several scenarios in which T-violating forces could lead to an organized state in the early Universe, starting from a still earlier disorganized state.