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Chaotic Entanglement: Entropy and Geometry.

Matthew A Morena¹, Kevin M Short²

¹Department of Mathematics, Christopher Newport University, Newport News, VA 23606, USA.

Entropy (Basel, Switzerland)

|October 23, 2021

Summary

This summary is machine-generated.

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Chaotic entanglement creates stable, self-sustaining pairs of chaotic systems, mimicking quantum entanglement. This process reverses entropy, decreasing it to zero as systems stabilize onto periodic orbits.

Area of Science:

Complex Systems
Nonlinear Dynamics
Chaos Theory

Background:

Classical chaotic systems typically exhibit unpredictable behavior.
Quantum entanglement involves correlated states of quantum systems.
Previous research has not explored entanglement-like phenomena in classical chaos.

Purpose of the Study:

To investigate the phenomenon of chaotic entanglement in classical systems.
To analyze the role of entropy in this entanglement process.
To describe the emergent geometric structures of entangled chaotic systems.

Main Methods:

Analysis of interacting, classically-chaotic systems.
Examination of system stabilization onto unstable periodic orbits.
Study of symbolic dynamics for sustaining periodicity.

Keywords:

chaotic entanglement chaotic systems coherent structures cupolets entropy geometry lattices unstable periodic orbits

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Main Results:

Demonstration of mutual stabilization in pairs of chaotic systems without external control.
Observation of entropy reduction to zero in entangled systems, akin to quantum state collapse.
Identification of complex geometric structures, from lattices to intricate patterns, formed by entangled systems.

Conclusions:

Chaotic entanglement is a novel phenomenon where classical systems exhibit quantum-like correlations.
Entropy plays a critical role, reversing and decreasing to zero during stabilization.
Entangled chaotic systems self-organize into complex, ordered geometric structures.