Time in basic dynamic equations of physics

Background and Objectives: It is known that the dynamic equations of motion do not suppress the reverse flow of time. On the other hand, the physical theories of irreversible processes are consistent with the fact that time goes in one direction. This article attempts to find a forbiddance on the inverse of time in the dynamic equations of motion. Methods: Both inversion of time together with momentum inversion and time inversion together with reverse movement along a trajectory in phase space are considered. The equations for non relativistic and relativistic classical particles, the Schrodinger equation for a quantum particle, and the Maxwell equations for a free electromagnetic field are studied. Conclusion: It is concluded that the backward movement along the phase trajectory with a reversed time is impossible. A special example of the transformation of reversible motion to irreversible motion shows that there are both a transition to statistical behavior and a dynamic irreversible motion.