A method is proposed for describing the dynamics of systems of interacting particles in terms of an auxiliary field, which in the static mode is equivalent to given interatomic potentials, and in the dynamic mode is a classical relativistic composite field. It has been established that for interatomic potentials that admit the Fourier transform, the auxiliary field is a composition of elementary fields that satisfy the Klein-Gordon equation with a certain spectrum of complex masses. The interaction between particles carried by the auxiliary field is nonlocal both in space variables and in time. The temporal non-locality is due to the dynamic nature of the auxiliary field and can be described in terms of functional-differential equations of retarded type. Due to the finiteness mass of the auxiliary field, the delay in interactions between particles can be arbitrarily large. A qualitative analysis of the dynamics of few-body and many-body systems with retarded interactions has been carried out, and non-statistical mechanisms for both the thermodynamic behavior of systems and synergistic effects has been established. In particular, a microscopic non-statistical mechanism for establishing thermodynamic equilibrium is proposed. References [1] Zakharov, A.Y.; Zakharov, M.A. Microscopic Dynamic Mechanism of Irreversible Thermodynamic Equilibration of Crystals. Quantum Rep. 2021, 3, 724-730. https://doi.org/10.3390/quantum3040045 [2] Zakharov, A.Y.; Zubkov, V.V. Field-Theoretical Representation of Interactions between Particles: Classical Relativistic Probability-Free Kinetic Theory. Universe 2022, 8, 281. https://doi.org/10.3390/universe8050281 [3] Zakharov, A.Y. Field Form of the Dynamics of Classical Many- and Few-Body Systems: From Microscopic Dynamics to Kinetics, Thermodynamics and Synergetics. Quantum Rep. 2022, 4, 533-543. https://doi.org/10.3390/quantum4040038