Chaotic Entanglement: Entropy and Geometry

Abstract

In chaotic entanglement, pairs of interacting classically-chaotic systems are induced into a state of mutual stabilization that can be maintained without external controls and that exhibits several properties consistent with quantum entanglement. In such a state, the chaotic behavior of each system is stabilized onto one of the system’s many unstable periodic orbits (generally located densely on the associated attractor), and the ensuing periodicity of each system is sustained by the symbolic dynamics of its partner system, and vice versa. Notably, chaotic entanglement is an entropy-reversing event: the entropy of each member of an entangled pair decreases to zero when each system collapses onto a given period orbit. In this paper, we discuss the role that entropy plays in chaotic entanglement. We also describe the geometry that arises when pairs of entangled chaotic systems organize into coherent structures that range in complexity from simple tripartite lattices to more involved patterns. We conclude with a discussion of future research directions.

Cupolets: History, Theory, and Applications

“…Morena and Short then extended the original framework of chaotic entanglement so that it allows for the entanglement between more than two chaotic systems [75]. In the new framework, a given chaotic system can mutually stabilize with multiple other chaotic systems through localized interactions at specific locations of the attractors.…”

“…In addition to these similarities, Short and Morena also discussed several properties of quantum mechanics that are incompatible with classical, chaotic systems [11,75]. For starters, superposition in quantum mechanics pertains to the linear combinations of state vectors that separately satisfy Schrödinger's equation and that collectively describe the state of an associated quantum system.…”