E-LAB-03 · EntropyLab · April 2026

ENTRO-CORE

Regime-Dependent Entropy-Augmented Control for Dynamical Systems.
PID optimal in stable regimes, ENTRO-CORE effective near critical thresholds.

Ψ · Entropy State · Real-time Control Signal

0.34

STABILIZED · Hybrid Controller Active

💻 GitHub Repository 📦 pip install entro-core 📌 DOI: 10.5281/zenodo.19431029

01 · Key Finding

Entropy-based control is regime-dependent

PID remains optimal in stable linear systems (Ψ_final = 0.017).
ENTRO-CORE provides benefits near critical instability thresholds.
A hybrid regime-switching controller achieves robust performance across regimes.

Control Law · ENTRO-CORE v1

u(t) = w₁·σ(Ψ_norm - θ) + w₂·tanh(Ψ̇) + w₃·tanh(Ψ̈)

w₁=0.5 (Perception), w₂=0.3 (Reflex), w₃=0.2 (Intuition), θ=1.4

Hybrid Regime-Switching

u(t) = { u_PID(t) if Ψ < 1.7, u_ENTRO(t) if Ψ ≥ 1.7 }

Switching threshold Ψ_th = 1.7

02 · Hybrid Controller

Regime-Switching Architecture

Controller Final Ψ Outcome

Uncontrolled 1.943 Divergent

PID Only 1.943 Divergent

ENTRO-CORE v1 1.480 Partial mitigation

Hybrid (threshold=1.7) 0.339 Stabilized

# pip install entro-core
from entro_core.hybrid_controller import HybridController

controller = HybridController(threshold=1.7)
result = controller.step(psi=1.8)

# → Output
u(t) = 0.423 · Mode: ENTRO-CORE

03 · Validation Results

Near-Critical Performance

Controller Final Ψ (t=20s) Observation

Uncontrolled 0.053 Naturally stable

PID 0.017 Optimal convergence

ENTRO-CORE v1 -0.239 Mild overshoot

Hybrid (threshold=1.7) -0.012 Robust performance