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