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Life Against Heat Death

Michail A. Zak

Published Sep 1, 2016• 0 citations
OpenAlex

Abstract

This work is inspired by the discovery of a new class of dynamical system described by ODE coupled with their Liouville equation. These systems called self-controlled 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. The discovery of isolated dynamical systems that can decrease entropy in violation of the second law of thermodynamics, and resemblances of these systems to livings implies that Life can slow down heat death of the Universe, and that can be associated with the Purpose of Life.

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This work is inspired by the discovery of a new class of dynamical system described by ODE coupled with their Liouville equation. These systems called self-controlled 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. The discovery of isolated dynamical systems that can decrease entropy in violation of the second law of thermodynamics, and resemblances of these systems to livings implies that Life can slow down heat death of the Universe, and that can be associated with the Purpose of Life.

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Non-Quantum Systems with Interference of Probabilities.

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A new class of dynamical systems with a preset type of interference of probabilities is introduced. It is obtained from the extension of the Madelung equation by replacing the quantum potential with a specially selected feedback from the Liouville equation. It has been proved that these systems are different from both Newtonian and quantum systems, but they can be useful for modeling spontaneous collective novelty phenomena when emerging outputs are qualitatively different from the weighted sum of individual inputs. Formation of language and fast decision-making process as potential applications of the probability interference is discussed.

•Apr 1, 2014•0 citations
This work is inspired by the discovery of a new class of dynamical system described by ODE coupled with their Liouville equation. These systems called self-controlled 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. The discovery of isolated dynamical systems that can decrease entropy in violation of the second law of thermodynamics, and resemblances of these systems to livings implies that Life can slow down heat death of the Universe, and that can be associated with the Purpose of Life.
This work is inspired by the discovery of a new class of dynamical system described by ODE coupled with their Liouville equation. These systems called self-controlled 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. The discovery of isolated dynamical systems that can decrease entropy in violation of the second law of thermodynamics, and resemblances of these systems to livings implies that Life can slow down heat death of the Universe, and that can be associated with the Purpose of Life.
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.
Abstract The paper proposes a scenario of origin and emerging of intelligent life in Universe based upon the mathematical discovery of a new class of dynamical systems described by ordinary differential equation (ODE) coupled with their Liouville equation. These systems called self-controlled 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 and quantum-like properties such as randomness, entanglement and probability interference typical for quantum systems have been described. At the same time, these systems expose properties of livings: decomposition into motor and mental dynamics, the capability of self-identification and self-awareness, as well as self-supervision. But the most surprising discovery is the existence of a special sub-class, in which the dynamical systems can violate the second law of thermodynamics, and that makes them different from both Newtonian and quantum physics. This sub-class should be associated with intelligent livings due to capability to move from disorder to order without external help. Based upon the mathematical discovery described above, one can assume that there are good chances that similar dynamical systems representing intelligent livings exist in real physical world. This provides a reason for a ‘rehabilitation’ of the Maxwell demon and put it into physics of intelligent systems. Indeed, the Maxwell demon is implemented by the feedback from the Liouville equation to the original ODE, while this feedback is capable to rearrange the probability distribution against the second law of thermodynamics. In addition to that, the same feedback removes the entropy paradox by explaining high order in our surrounding by ‘intelligent life support’. Two-steps transition: from the Newtonian physics to the linear model of life, and from the latter to the model of intelligent life are analysed. The first transition is triggered by the Hadamard instability of the Newtonian physics with respect to small random disturbances in linear terms of the Liouville feedback. The second transition is triggered by instability of linear model of life with respect to small random disturbances of non-linear terms of Liouville feedback. This transition could be implemented by such physical phenomena as shock waves or negative diffusion in probability space. Both transitions can be associated with catastrophe theory, in which sudden shifts in behaviour arises from small changes in parameters of the model. In view of the proposed model, possible competition between artificial and human intelligence are discussed.
The challenge of this work is to connect quantum mechanics with the concept of intelligence. By intelligence we understand a capability to move from disorder to order without external resources, i.e. in violation of the second law of thermodynamics. The objective is to find such a mathematical object described by ODE that possesses such a capability. The proposed approach is based upon modification of the Madelung version of the Schrodinger equation by replacing the force following from quantum potential with non-conservative forces that link to the concept of information. A mathematical formalism suggests that a hypothetical intelligent particle, besides the capability to move against the second law of thermodynamics, acquires such properties like self-image, self-awareness, self- supervision, etc. that are typical for Livings. However since this particle being a quantum-classical hybrid acquires non-Newtonian and non-quantum properties, it does not belong to the physics matter as we know it: the modern physics should be complemented with the concept of an information force that represents a bridge to intelligent particle. It has been suggested that quantum mechanics should be complemented by the intelligent particle as an independent entity, and that will be the necessary step to physics of Life. At this stage, the intelligent particle is introduced as an abstract mathematical concept that is satisfied only mathematical rules and assumptions, and its physical representation is still an open problem.
The challenge of this paper is to relate quantum-inspired dynamics represented by a self- supervised system, to solutions of noncomputable problems. In the self-supervised systems, the role of actuators is played by the probability produced by the corresponding 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 in [1]. It has been demonstrated there, that such systems exist in the mathematical world: they are presented by ODE coupled with their Liouville equation, but they belong neither to Newtonian nor to quantum physics. The central point of this paper is the application of the self-supervised systems to solve traveling salesman problem.
A new class of dynamical systems with a preset type of interference of probabilities is introduced. It is obtained from the extension of the Madelung equation by replacing the quantum potential with a specially selected feedback from the Liouville equation. It has been proved that these systems are different from both Newtonian and quantum systems, but they can be useful for modeling spontaneous collective novelty phenomena when emerging outputs are qualitatively different from the weighted sum of individual inputs. Formation of language and fast decision-making process as potential applications of the probability interference is discussed.