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.
Highlights
In a series of recent papers, it has been shown that chaotic systems can be stabilized onto periodic orbits through the imposition of a control scheme that applies a set of impulsive kicks to the chaotic system along control planes or Poincaré sections that intersect the attractor of the system
Cupolets are a new class of waveforms that can be isolated from a given chaotic system through a control mechanism that stabilizes the normally-unstable periodic orbits of the chaotic system
In a recent series of papers [14,15,21], it is shown that pairs of chaotic systems that are capable of producing cupolets may be able to interact in a way that causes them to chaotically entangle, by which we mean that through their interaction they fall into a state of mutual stabilization onto their cupolets
Summary
In a series of recent papers, it has been shown that chaotic systems can be stabilized onto periodic orbits through the imposition of a control scheme that applies a set of impulsive kicks to the chaotic system along control planes or Poincaré sections that intersect the attractor of the system. The robust stabilization property allowed the transmitter and receiver to be initialized into the same state [2,3] Further development along these lines led to the creation of a remote key generation scheme that addresses the problem of key distribution in standard secure communication approaches [4,5]. Further investigation revealed that certain cupolets could be defined as fundamental and others as composite, with the fundamental cupolets irreducible within a finite space of cupolets [13] After this preliminary work, the question arose whether interacting chaotic systems could ever lock into mutually stabilizing periodic orbits, where the interaction would be mediated by a fixed exchange function. Chaotic entanglement is an entropy-reversing event, which is unusual in classical mechanics
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