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Entanglement of Memories and Reality in Models of Livings

Michail A. Zak

Published Jan 1, 2012• 1 citation
OpenAlex

Abstract

Abstract: This paper discusses quantum-inspired models of Livings from the viewpoint of the second law of thermodynamics. It concentrates on Hadamard’s instability of the corresponding parabolic PDE for motions against the time arrow. The instability is removed by adding imaginary components to state variables. The evolution from present to past in a virtual (mental) space is interpreted as memories of the Livings under consideration. Quantum-like entanglement of memories and real motions are found and discussed.

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•Nov 28, 2025•0 citations
Abstract: This paper discusses quantum-inspired models of Livings from the viewpoint of the second law of thermodynamics. It concentrates on Hadamard’s instability of the corresponding parabolic PDE for motions against the time arrow. The instability is removed by adding imaginary components to state variables. The evolution from present to past in a virtual (mental) space is interpreted as memories of the Livings under consideration. Quantum-like entanglement of memories and real motions are found and discussed.
This paper discusses quantum-inspired models of Livings from the viewpoint of information processing. The model of Livings consists of motor dynamics simulating actual behavior of the object, and mental dynamics representing evolution of the corresponding knowledge-base and incorporating it in the form of information flows into the motor dynamics. Due to feedback from mental dynamics, the motor dynamics attains quantum-like properties: its trajectory splits into a family of different trajectories, and each of those trajectories can be chosen with the probability prescribed by the mental dynamics The paper concentrates on discovery of a new type of entanglement that correlates the probabilities of actions of Livings rather than the actions themselves.
Abstract If an asymmetry in time does not arise from the fundamental dynamical laws of physics, it may be found in special boundary conditions. The argument normally goes that since thermodynamic entropy in the past is lower than in the future according to the Second Law of Thermodynamics, then tracing this back to the time around the Big Bang means the universe must have started off in a state of very low thermodynamic entropy: the Thermodynamic Past Hypothesis. In this paper, we consider another boundary condition that plays a similar role, but for the decoherent arrow of time, i.e. the subsystems of the universe are more mixed in the future than in the past. According to what we call the Entanglement Past Hypothesis, the initial quantum state of the universe had very low entanglement entropy. We clarify the content of the Entanglement Past Hypothesis, compare it with the Thermodynamic Past Hypothesis, and identify some challenges and open questions for future research.
Abstract This work is inspired by the discovery of a new class of dynamical system described by ordinary differential equations 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 living systems. 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 suggests that ‘Life’ can slow down the ‘heat death’ of the Universe and that can be associated with the Purpose of Life.
The paper extends the mathematical formalism of quantum physics to include games of intelligent agents that communicate due to entanglement. The novelty of the approach is based upon a human factor-based behavioral model of an intelligent agent. The model is quantum inspired: it is represented by a modified Madelung equation in which the gradient of quantum potential is replaced by a specially chosen information force. It consists of motor dynamics simulating actual behavior of the agent, and mental dynamics representing evolution of the corresponding knowledge base and incorporating this knowledge in the form of information flows into the motor dynamics. Due to feedback from mental dynamics, the motor dynamics attains quantum-like properties: its trajectory splits into a family of different trajectories, and each of those trajectories can be chosen with the probability prescribed by the mental dynamics; each agent is entangled (in a quantum way) to other agents and makes calculated predictions for future actions; human factor is associated with violation of the second law of thermodynamics: the system can move from disorder to order without external help, and that represents intrinsic intelligence. All of these departures actually extend and complement the classical methods making them especially successful in analysis of communications of agents represented by new mathematical formalism, and in particular, in agent-based economics with a human factor.
The concept of time presents a profound challenge at the intersection of quantum mechanics and thermodynamics. While fundamental microscopic laws are largely time-symmetric, macroscopic phenomena universally exhibit a distinct thermodynamic arrow of time, characterized by increasing entropy. This paper explores the hypothesis that quantum entanglement plays a crucial role in the emergence of this thermodynamic arrow. We review how the entanglement between a quantum system and its environment leads to decoherence, effectively driving the system towards a state of higher entropy and classical-like behavior. By analyzing concepts such as von Neumann entropy, entanglement entropy, and the Page-Wootters mechanism, we propose a theoretical framework where the degradation and spreading of entanglement act as the underlying mechanism for the perceived unidirectional flow of time. This approach offers a potential resolution to the "problem of time" in quantum gravity and provides a unified perspective on the genesis of irreversibility from the inherently reversible laws of quantum mechanics. We discuss the implications of this entanglement-driven temporal emergence for our understanding of the universe's initial low-entropy state and the fundamental nature of reality.