Control of multiscale systems wish constraints 1. Basic principles of concept of evolution of systems with varying constraints

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

“…The importance of the notion of nonlocality for the theory of self-organizaltion was indicated in the first work of the cycle [1]. Here, we will refine the connection of the property of nonlocality of the wave functions determined from the Schrödinger equation (see [12]) with mass and entropic forces and will show that this property is also revealed in classical physics as a result of the geometrization of the physical processes of dynamics and evolution.…”

“…Thus, the dominating mass force (general dominating perturbation) [5] supplies coherently the momentum p sn of a directed motion to all elements of the ensemble of particles, which meets the condition N n=1 p sn P Tmax , where P Tmax is the maximal absolute value of the momentum of the intrinsic heat motion of any of the elements of the ensemble (MQO, in this case). The principle of dynamical harmonization [1] implies that the evolution of a self-organizing system is possible only in the presence of the coherent acceleration of the entire system, when all particles of the system acquire the same momentum increment due to the action of the entropic force arising under the nonzero entropy gradient. In this case, it is necessary that the regular component of the change in the momenta of particles Δp S at the expense of the entropy exceed the chaotic heat component p T ≈ m u T .…”

“…where the dot stands for the differentiation with respect to the time. Hence, the entropic force is proportional to the entropy production gradient σ S = Ṡ (see also [1]) in the system. This formula differs from that obtained by E. Verlinde [35], who used the equations of equilibrium thermodynamics of closed systems and obtained…”

“…This work is a sequel of the cycle of works (see [1][2]), where some approach to the control over the evolution of the systems of many particles on the basis of the general variational principle of self-organization (the principle of dynamical harmonization of systems) is presented. The purpose of the cycle is the development of foundations of the theory and the technology of the synthesis of final states of a system of particles with desired structure and energy binding, which are attained from a given initial state with the help of the initiation of a natural evolution and the control over an evolutionary trajectory of the system at the expense of its internal power resources at a minimal use of the energy of external drivers.l…”

“…The principle of dynamical harmonization [1,5] asserts that the selforganization of a system of particles, being under the action of mass forces leading to coherent accelerations of all particles of the system, is directed always to the realization of the transition from the initial state to a state with maximally free dynamics by means of changes of the structure of the system and its inertia relative to mass forces.…”