🔴 ENTRO-ENGINE — Entropy Flow Regulator for Coupled Intelligence Systems

"A single engine regulates itself. A fleet of engines requires a coordinator." — Samir Baladi, April 2026

ENTRO-ENGINE is the fourth project of the EntropyLab research program (E-LAB-04).
It advances from single-system entropy control to multi-system entropy coordination — distributing thermodynamic pressure across coupled subsystems under a shared global budget constraint.

---

📌 DOI & Badges

---

🌐 Official Website

https://entro-engine.netlify.app

---

🎯 Vision

Build a coordination layer for AI pipelines in which multiple entropy-generating subsystems share a common thermodynamic budget — ensuring that no single subsystem collapses under load while others operate at idle, and that corrective pressure is distributed in proportion to each subsystem's entropy contribution.

The Core Shift

Architecture	Scope	Objective
ENTROPIA (E-LAB-01)	Definition	Establish Ψ vocabulary
ENTRO-AI (E-LAB-02)	Measurement	Monitor & detect collapse
ENTRO-CORE (E-LAB-03)	Local Control	Stabilize single Ψ field
ENTRO-ENGINE (E-LAB-04)	Coordination	Distribute pressure across coupled systems

---

🔬 Key Innovation

Instead of: Each subsystem independently minimizes its own entropy
ENTRO-ENGINE does: Enforce a global entropy budget across all coupled subsystems

Ψ_total(t) = Ψ_scraper + Ψ_llm ≤ Ψ_budget   ∀t

The engine computes corrective signals proportional to each subsystem's entropy fraction:

u_i(t) = −α · ρ_i(t) · tanh(β · Δ(t))

Where:

• ρ_i = fractional entropy ratio (fairness principle)
• Δ(t) = global entropy pressure above budget
• tanh = saturation (prevents overcorrection)

---

📊 Architecture

entro-engine/
│
├── engine/                   # Core coordination engine
│   ├── controller.py         # ENTRO-ENGINE control law (Eq. 14)
│   ├── budget.py             # Entropy budget constraint (Eq. 9–11)
│   └── allocator.py          # Proportional allocation ratios (Eq. 12–13)
│
├── subsystems/               # Coupled subsystem models
│   ├── scraper.py            # Scraper entropy source (Eq. 1, 4, 6)
│   ├── llm_queue.py          # LLM processing queue (Eq. 2, 5, 7)
│   └── base.py               # Abstract subsystem interface
│
├── entropy/                  # Entropy formulation layer
│   ├── proxy.py              # Log-proxy functions: Ψ = log(1 + x)
│   ├── aggregator.py         # Global Ψ_total computation (Eq. 8)
│   └── normalizer.py         # Logistic normalization
│
├── pipeline/                 # Realistic pipeline simulation
│   ├── simulator.py          # Three-phase pipeline (warmup / surge / recovery)
│   ├── simulator_v9.py       # Balanced regime engine
│   └── simulator_v10.py      # Recursive attractor engine
│
├── reports/                  # Daily/Weekly/Monthly reports
│   ├── daily/                # Daily .txt reports
│   ├── weekly/               # Weekly summaries
│   ├── monthly/              # Monthly analyses
│   └── alerts/               # Alert logs
│
├── tests/                    # Unit & integration tests
│   ├── test_controller.py    # Controller tests (9/9 passed)
│   ├── test_allocator.py     # Allocator tests
│   └── test_integration.py   # Integration tests
│
├── data/                     # Simulation output datasets
│   └── simulation_runs/      # CSV trajectory files
│
├── docs/                     # Documentation
├── paper/                    # Research paper assets
├── AUTHORS.md
├── CHANGELOG.md
├── LICENSE
├── README.md
└── pyproject.toml

---

⚙️ Core Equations

Eq.	Expression	Description
6	Ψ_s(t) = log(1 + r_s(t))	Scraper entropy proxy
7	Ψ_l(t) = log(1 + q_l(t))	LLM entropy proxy
8	Ψ_total(t) = Ψ_s + Ψ_l	Global entropy aggregate
9	Ψ_total(t) ≤ Ψ_budget ∀t	Budget constraint
11	Δ(t) = Ψ_total(t) − Ψ_budget	Entropy pressure
12–13	ρ_i = Ψ_i / Ψ_total	Proportional allocation ratios
14	u_i(t) = −α · ρ_i · tanh(β · Δ)	ENTRO-ENGINE control law

---

📦 Installation

pip install entro-engine

From source:

git clone https://gitlab.com/gitdeeper10/entro-engine.git
cd entro-engine
pip install -e .

---

🚀 Quick Start

from entro_engine import ENTROEngineController

# Initialize controller
controller = ENTROEngineController(alpha=0.5, beta=2.0, psi_budget=3.0)

# Compute control signal
signal = controller.compute_control(psi_i=1.5, psi_total=4.0)

print(f"u = {signal.u:.3f}")
print(f"ρ = {signal.rho:.3f}")
print(f"Δ = {signal.delta:.3f}")

---

📈 Simulation Results

Validated on a three-phase realistic pipeline (warmup → surge → recovery):

Metric Uncontrolled ENTRO-ENGINE Improvement Budget violations 312 / 1000 12 / 1000 96.2% reduction Peak Ψ_total 5.84 3.31 43.3% reduction Peak LLM queue 87.6 req 23.4 req 73.3% reduction

Regime Distribution (v9 Final Run)

Regime Count Percentage 🟢 Stable 24 30.0% 🟡 Stress 19 23.75% 🔴 Critical 37 46.25%

---

🔗 Links

Resource URL 🌐 Official Website https://entro-engine.netlify.app 📊 Dashboard https://entro-engine.netlify.app/dashboard 📚 Documentation https://entro-engine.netlify.app/documentation 📋 Reports https://entro-engine.netlify.app/reports 🦊 GitLab (Primary) https://gitlab.com/gitdeeper10/entro-engine 💻 GitHub (Mirror) https://github.com/gitdeeper10/entro-engine 📦 PyPI https://pypi.org/project/entro-engine 📌 DOI https://doi.org/10.5281/zenodo.19441032 🔴 ENTROPIA (E-LAB-01) https://doi.org/10.5281/zenodo.19416737 ⚙️ ENTRO-AI (E-LAB-02) https://doi.org/10.5281/zenodo.19284086 🧠 ENTRO-CORE (E-LAB-03) https://doi.org/10.5281/zenodo.19431029 👤 ORCID https://orcid.org/0009-0003-8903-0029

---

🗺️ EntropyLab Research Program

Project Title Status DOI E-LAB-01 ENTROPIA: Thermodynamic-Information Unification ✅ Published 10.5281/zenodo.19416737 E-LAB-02 ENTRO-AI: Entropy-Resistant AI Architectures ✅ Published 10.5281/zenodo.19284086 E-LAB-03 ENTRO-CORE: Self-Regulated Intelligence ✅ Published 10.5281/zenodo.19431029 E-LAB-04 ENTRO-ENGINE: Entropy Flow Regulator ✅ Published 10.5281/zenodo.19441032 E-LAB-05 ENTRO-FIN: Financial Market Entropic Signatures 📋 Planned — E-LAB-06 ENTRO-SOCIAL: Social Network Information Cascades 📋 Planned — E-LAB-07 ENTRO-QUANTUM: Quantum Extension 📋 Planned — E-LAB-08 ENTRO-BIO: Biological Neural Networks 📋 Planned — E-LAB-09 ENTRO-MANIFESTO: Unified Research Manifesto 📋 Planned —

---

📄 Citation

@software{baladi2026entroengine,
  author    = {Baladi, Samir},
  title     = {ENTRO-ENGINE: Entropy Flow Regulator for Coupled Intelligence Systems},
  year      = {2026},
  version   = {1.0.0},
  doi       = {10.5281/zenodo.19441032},
  url       = {https://gitlab.com/gitdeeper10/entro-engine},
  note      = {E-LAB-04. Builds on E-LAB-01, E-LAB-02, E-LAB-03}
}

---

📜 License

MIT License — Copyright © 2026 Samir Baladi

---

Part of the EntropyLab ten-project research program "Intelligence by Design, Stability by Physics"