The c-Entropy of non-dissipative L-systems

TL;DR

This work extends the c-Entropy framework to canonical L-systems with non-dissipative state-space operators, deriving explicit closed-form expressions for c-Entropy in both dissipative and non-dissipative settings. It constructs two-dimensional L-systems using multiplication-type main operators, obtains matrix-valued transfer and impedance functions, and analyzes system coupling to prove additivity of c-Entropy under composition. The paper also generalizes dissipation and accumulation coefficients within these models and provides concrete examples illustrating extreme and finite entropy values and the corresponding coefficients. Overall, the results clarify energy-coupling behavior in L-systems and enhance spectral/impedance perspectives for non-dissipative dynamics.

Abstract

In this paper, we extend the definition of c-entropy to canonical L-systems with non-dissipative state-space operators. We also introduce the concepts of dissipation and accumulation coefficients for such systems. In addition, we examine the coupling of these L-systems and derive closed form expressions for the corresponding c-entropy.

Figures (2)

• Figure 1: Maximal c-Entropy of a dissipative L-system
• Figure 2: Minimal c-Entropy of an accumulative L-system

Theorems & Definitions (23)

• Definition 1
• Theorem 2
• proof
• Theorem 3
• proof
• Theorem 4
• proof
• Theorem 5
• proof
• Theorem 6