Dual characterization of critical fluctuations: Density functional theory & nonlinear dynamics close to a tangent bifurcation

TL;DR

This paper explores the connection between critical fluctuations in thermal systems and intermittency in low-dimensional chaos, using density functional theory and renormalization group methods for a unified, formal understanding.

Contribution

It introduces a formal framework linking density functional theory and nonlinear dynamics to describe critical phenomena and chaos onset.

Findings

Establishes a correspondence between critical clusters and chaos intermittency.

Integrates density functional formalism with RG fixed-point maps.

Provides a unified theoretical approach to high- and low-dimensional phenomena.

Abstract

We improve on the description of the relationship that exists between critical clusters in thermal systems and intermittency near the onset of chaos in low-dimensional systems. We make use of the statistical-mechanical language of inhomogeneous systems and of the renormalization group (RG) method in nonlinear dynamics to provide a more accurate, formal, approach to the subject. The description of this remarkable correspondence encompasses, on the one hand, the density functional formalism, where classical and quantum mechanical analogues match the procedure for one-dimensional clusters, and, on the other, the RG fixed-point map of functional compositions that captures the essential dynamical behavior. We provide details of how the above-referred theoretical approaches interrelate and discuss the implications of the correspondence between the high-dimensional (degrees of freedom) phenomenon and low-dimensional dynamics.