Attractor-driven matter

TL;DR

This paper introduces a novel class of matter called attractor-driven matter, where particles' internal states are modeled by points on strange attractors, enabling complex and emergent behaviors in classical particle systems.

Contribution

It proposes a new formalism for modeling particles with internal states on attractors, extending the concept of matter to include attractor-driven dynamics and exploring their potential for complex behavior.

Findings

Formalism for attractor-driven matter outlined

Examples show resemblance to active matter behaviors

Potential broad applicability to complex dynamical systems

Abstract

The state of a classical point-particle system may often be specified by giving the position and momentum for each constituent particle. For non-pointlike particles, the center-of-mass position may be augmented by an additional coordinate that specifies the internal state of each particle. The internal state space is typically topologically simple, in the sense that the particle's internal coordinate belongs to a suitable symmetry group. In this paper we explore the idea of giving internal complexity to the particles, by attributing to each particle an internal state space that is represented by a point on a strange (or otherwise) attracting set. It is of course very well known that strange attractors arise in a variety of nonlinear dynamical systems. However, rather than considering strange attractors as emerging from complex dynamics, we may employ strange attractors to {\em drive} such dynamics. In particular, by using an attractor (strange or otherwise) to model each particle's internal state space, we present a class of matter coined ``attractor-driven matter''. We outline the general formalism for attractor-driven matter and explore several specific examples, some of which are reminiscent of active matter. Beyond the examples studied in this paper, our formalism for attractor-driven dynamics may be applicable more broadly, to model complex dynamical and emergent behaviors in a variety of contexts.