The dynamics of free and forced vibrations of a chain of atoms is investigated in a harmonic model taking into account the retardation of interactions between atoms. It is shown that, depending on the type of interatomic interactions, free vibrations either damp out or increase infinitely. Forced oscillations in the first case, regardless of the initial conditions, pass into a stationary regime, which is interpreted as a transition to a state of dynamic equilibrium between the crystal and the field. A non-statistical dynamic mechanism of the irreversible process of establishing a state of thermodynamic equilibrium is proposed. This work is devoted to the study of the influence of the retardation of interatomic interactions on the dynamics of a one-dimensional crystal lattice in order to find a microscopic dynamic substantiation of the mechanism for achieving thermodynamic equilibrium in a system of particles. The main results of this work are as follows. 1. It is found that the retardation of interactions between particles leads to a radical restructuring of the dynamics of a one-dimensional harmonic chain. In particular, due to the retardation of interactions, stationary free oscillations in the chain are impossible. 2. Since the presence of free oscillations with increasing amplitudes means the destruction of the chain, a criterion for the absence of growing oscillations in the system was obtained. This criterion is a condition for the stability of the chain. 3. It is shown that when a stable chain of particles with retarded interactions between them is immersed in an alternating external field, the system passes into a stationary state, which depends both on the properties of the system and on the characteristics of the external field. This stationary state has been interpreted as a dynamic equilibrium between chain and an external field.