Authors: Michail Zak
A new class of dynamical system described by ODE coupled with their Liouville equation has been introduced and discussed. These systems called self-controlled, or self-supervised since the role of actuators is played by the probability produced by the Liouville equation. Following the Madelung equation that belongs to this class, non- Newtonian properties such as randomness, entanglement, and probability interference typical for quantum systems have been described. Special attention was paid to the capability to violate the second law of thermodynamics, which makes these systems neither Newtonian, nor quantum. It has been shown that self-controlled dynamical systems can be linked to mathematical models of livings as well as to models of AI. The central point of this paper is the application of the self-controlled systems to NP-complete problems known as being unsolvable neither by classical nor by quantum algorithms. The approach is illustrated by solving a search in unsorted database in polynomial time by resonance between external force representing the address of a required item and the response representing location of this item.
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