Dissipation and c-Entropy in Nevanlinna-Pick Interpolation

TL;DR

This paper investigates the structural and quantitative properties of interpolation L-systems for finite Nevanlinna-Pick data, deriving explicit formulas for key invariants related to dissipation and entropy.

Contribution

It introduces explicit formulas for c-entropy and dissipation coefficients, linking geometric node placement to the dynamical properties of interpolation L-systems.

Findings

Explicit formulas for c-entropy and dissipation coefficient.

Maximal invariants occur for purely imaginary nodes.

Symmetric configurations yield explicit rational impedance functions.

Abstract

We study interpolation L-systems realizing finite Nevanlinna-Pick data sets and analyze their structural and quantitative characteristics. Explicit formulas are derived for the c-entropy and dissipation coefficient, two intrinsic invariants that describe the dissipative structure of interpolation L-systems. These quantities depend only on the geometric placement of interpolation nodes in $\mathbb{C}_+$, attaining maximal finite values for purely imaginary nodes. The interpolation model $\Theta_\Delta$ and its unitary equivalents reveal that these invariants form a direct link between analytic interpolation data and the dynamical properties of L-systems. Particular attention is given to symmetric configurations, where the impedance function admits an explicit rational representation and a natural physical interpretation in terms of equivalent $LC$-networks.