Control over multiscale systems with constraints. 3. Geometrodynamics of the evolution of systems with varying constraints

TL;DR

This paper explores a geometric variational principle to control the evolution of many-particle systems with varying constraints, linking nonlocality, coherence, and space-time curvature to self-organization and synthesis of new structures.

Contribution

It introduces a geometric approach based on the principle of dynamical harmonization, connecting quantum nonlocality and coherence with macroscopic self-organization in constrained systems.

Findings

Nonlocality and coherence relate to mass entropic forces.

Space-time curvature influences the synthesis of new structures.

Electromagnetic fields can initiate self-organizing processes.

Abstract

With the use of the general variational principle of self-organization of systems with varying constraints, namely the principle of dynamical harmonization of systems presented in the first work of the cycle, we advance an approach to the control over the evolution of systems of many particles. The geometric nature of this principle is analyzed. On the basis of the de Broglie--Bohm representation of the Schr\"odinger equation, we establish a connection of the nonlocality and the coherence of the systems of many particles with mass entropic forces. The defining role of a coherent acceleration and a space-time curvature in the control over the synthesis of new structures in systems with varying constraints is demonstrated. The basic criteria for electromagnetic fields to initiate the processes of self-organizing synthesis and for the quantum properties of a nonlocality on macroscopic scales, which are necessary for the self-organizing synthesis, are formulated.