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.