Uncertainty relation and quantitative condition of inversion symmetry of   time in many-particle system
  We proved that the uncertainty relation fits in with many-particle system and the equality of the relation corresponds to the thermodynamic equilibrium state, the inequality of the relation corresponds to the thermodynamic non-equilibrium state for any quantum system. The microscopic origin of the second law of thermodynamics is certainly resulted in the wave-particle duality of matter. A quantitative condition of inversion symmetry of time is obtained. 
You-gang Feng