L-systems with Multiplication Operator and c-Entropy
Sergey Belyi, Konstantin Makarov, Eduard Tsekanovskii
TL;DR
The paper develops a systematic framework for L-systems built from a scalar multiplication operator, focusing on c-entropy and the dissipation coefficient. It provides explicit transfer and impedance formulas, classifies impedance functions within bounded Donoghue classes, and analyzes the stability of these classes under coupling. A detailed treatment of both standard and skew-adjoint L-systems reveals additive properties of c-entropy and a hierarchical rule for dissipation under coupling. The results are complemented by concrete examples and a skew-adjoint coupling interpretation via LC-circuit analogies, offering a principled approach to impedance realization within Donoghue classes and their multiplicative couplings.
Abstract
In this note, we utilize the concepts of c-entropy and the dissipation coefficient in connection with canonical L-systems based on the multiplication (by a scalar) operator. Additionally, we examine the coupling of such L-systems and derive explicit formulas for the associated c-entropy and dissipation coefficient. In this context, we also introduce the concept of a skew-adjoint L-system and analyze its coupling with the original L-system.