The Irreversibility of Microscopic Motions

People have long had a problem: the equations of motion that reflect the laws of physics are invariance under time inversion, while there always are irreversible processes for gases compose of microscopic particles. This article solves this problem. The point is that we should distinguish between the concepts of the equation of motion and motion. We also need to distinguish between the concepts of time-inverse motion and reverse motion. The former is anticlockwise, which is a frictional motion, while the latter is clockwise. For the single-particle motions in classical mechanics and in quantum mechanics, we present mathematical expressions for time-inversion motion and reverse motion, respectively. We demonstrate that single-particle motion is irreversible. The definition of the reversibility of two-particle collisions is given. According to the definition, the two-particle collision as a microscopic motion processes is irreversible. Consequently, for a gas consisting of a large number of particles colliding with each other, its movement should be irreversible, unless the condition of detailed balance is met. We give a physical explanation for the detailed balance, which does not concern the meaning of microscopic reversibility. The detailed balance means that after a pair of reciprocal collisions occur, the distribution function of the particles remains unchanged. Therefore, microscopic two-particle collision events are irreversible, but the statistical average of a large number of collision events makes it possible for the macroscopic process of a gas to be reversible. Conclusively, we clarify the microscopic mechanism of the irreversible process of gases.