Classical many-body theory with retarded interactions: Dynamical irreversibility and determinism without probabilities

•A new form of equation of motion of classical many-body system is proposed.•Interactions retardation as one of the mechanisms of many-body system irreversibility.•Irreversibility and determinism without probabilities.•The possible way to microscopic foundation of thermodynamics.

The exact equations of motion for microscopic density of classical many-body system with account of inter-particle retarded interactions is derived. It is shown that interactions retardation leads to irreversible behavior of many-body systems.