🔴 Overview
From classical deterministic to quantum-inspired probabilistic
"True intelligence is not the elimination of uncertainty — it is the art of acting optimally within it." — Samir Baladi, April 2026
ENTRO-QUANTUM extends classical entropy control to quantum-inspired probabilistic mechanics. The system's stability is represented as a wavefunction — a complex-valued probability amplitude over possible futures — that collapses to a classical scalar only at inference time. Built upon ENTRO-NET (E-LAB-06), this work demonstrates that uncertainty is not a liability but a resource.
55
Unit Tests
100% pass rate
19+
Equations
Sections 3.1-3.19, 4.1-4.3
7
Core Modules
Complete implementation
0.05
Uncertainty Bound
κ_E/2 = 0.05
Ψ-W(s,t)
Entropic Wavefunction
Ψ-W(s, t) : S × R⁺ → ℂ
P(s, t) = |Ψ-W(s, t)|² (Born rule)
⟨Ψ⟩(t) = ∫ s · |Ψ-W(s,t)|² ds
psi = EntropicWavefunction(resolution=100)
psi.gaussian_initial(mean=0.339, variance=0.05)
entropy_state = psi.expectation_value()
collapse_prob = psi.collapse_probability(critical_threshold=0.8)
| Method | Description | Equation |
|---|
| probability_density(i) | |Ψ|² at grid point | Eq 3.2 |
| expectation_value() | ∫ s·|Ψ|² ds | Eq 3.3 |
| normalize() | ∫ |Ψ|² ds = 1 | — |
| collapse_probability() | P(s ≥ s_critical) | — |
H_E
Entropic Hamiltonian
i·ħ_E · ∂Ψ/∂t = H_E · Ψ
H_E = T_E + V_AEW + V_ext
T_E = -(ħ_E²/2m_E) · ∂²/∂s²
V_AEW = ½·ω_E²·(s - s_target)²
H = EntropicHamiltonian(hbar_E=0.1, m_E=1.0, omega_E=2.0, target=0.339)
h_real, h_imag = H.apply(psi_real, psi_imag, s_grid, ds, t)
ΔΨ·ΔM ≥ κ_E/2
Entropic Uncertainty Principle
[S_op, P_E] = i·ħ_E
σ_S · σ_P ≥ ħ_E / 2
ΔΨ · ΔM ≥ κ_E / 2 (where κ_E = ħ_E / m_E)
α* = 1/(2 - P_collapse)
G = α²·|⟨Ψ|Π_s|Ψ⟩|² (information gain)
D = α·(1-α)·Var[S] (measurement disturbance)
E_ij
Informational Entanglement
Ψ-W_joint(s_1, s_2, ..., s_N, t)
E_ij = I(S_i ; S_j) / min[H(S_i), H(S_j)]
I(S_i ; S_j) = H(S_i) + H(S_j) - H(S_i, S_j)
S_ent = -Tr[ρ_A log ρ_A]
Q_k
Quantum Jump Operator
Ψ-W(s, t+dt) = Q_k·Ψ-W(s,t) / ||Q_k·Ψ-W(s,t)||
Σ_k Q_k†Q_k + i(H_E† - H_E) = 0
H_eff = H_E - (iħ/2)·Σ Q_k†Q_k
🤫 SOP
Silent Observer Protocol
AMBIENT: α = 0.8 (P_collapse < 0.05)
ADVISORY: α = 0.3 (0.05 ≤ P_collapse < 0.30)
SILENT_WATCH: α = α* (0.30 ≤ P_collapse < 0.90)
CONTROLLED_COLLAPSE: α → 0 (P_collapse ≥ 0.90)
measured_s, new_real, new_imag = observer.weak_measure(real, imag, s_grid, alpha)
🎲 QMC
Quantum Monte Carlo Simulator
simulator = QuantumMonteCarloSimulator(
resolution=100, hbar_E=0.1, m_E=1.0,
omega_E=2.0, target=0.339, n_nodes=3
)
history = simulator.evolve(steps=500, record_interval=50)
results = simulator.get_results()
📦 Installation
Quick setup
pip install entro-quantum
git clone https://github.com/gitdeeper10/ENTRO-QUANTUM.git
cd ENTRO-QUANTUM
pip install -r requirements.txt
pip install -e .
python -c "from entro_quantum import __version__; print(__version__)"
🔧 API Reference
Python interface
EntropicWavefunction
Complex-valued probability amplitude over stability states
from entro_quantum import EntropicWavefunction
psi = EntropicWavefunction(resolution=100, s_max=1.0)
psi.gaussian_initial(mean=0.339, variance=0.05)
exp_val = psi.expectation_value()
EntropicHamiltonian
Entropic Hamiltonian H_E = T_E + V_AEW + V_ext
from entro_quantum import EntropicHamiltonian
H = EntropicHamiltonian(hbar_E=0.1, m_E=1.0, omega_E=2.0, target=0.339)
h_real, h_imag = H.apply(real, imag, s_grid, ds, t)
EntropicUncertainty
Entropic Uncertainty Principle ΔΨ·ΔM ≥ κ_E/2
from entro_quantum import EntropicUncertainty
unc = EntropicUncertainty(hbar_E=0.1, m_E=1.0)
bound = unc.uncertainty_bound()
alpha = unc.optimal_measurement_strength(p_collapse=0.3)
InformationalEntanglement
Entanglement tensor E_ij for distributed nodes
from entro_quantum import InformationalEntanglement
ent = InformationalEntanglement(n_nodes=3)
ent.record_state(node_id, psi)
ent.update_tensor()
e_ij = ent.get_entanglement(i, j)
QuantumJumpOperator
Quantum jump operator Q_k for discontinuous collapse
from entro_quantum import QuantumJumpOperator
jump = QuantumJumpOperator(num_jumps=3, gamma=0.01)
new_real, new_imag = jump.apply_jump(real, imag, jump_idx=0)
SilentObserver
Silent Observer Protocol for weak measurement
from entro_quantum import SilentObserver
observer = SilentObserver()
alpha = observer.measurement_strength(p_collapse=0.5)
measured_s, new_real, new_imag = observer.weak_measure(real, imag, s_grid, alpha)
🧩 Core Modules
ENTRO-QUANTUM architecture
wavefunction.py
Ψ-W(s,t)
Entropic wavefunction
hamiltonian.py
H_E
Entropic Hamiltonian
uncertainty.py
ΔΨ·ΔM ≥ κ_E/2
Uncertainty principle
entanglement.py
E_ij
Entanglement tensor
quantum_jump.py
Q_k
Quantum jump operator
silent_observer.py
SOP
Silent Observer Protocol
simulator.py
QMC
Quantum Monte Carlo
👤 Author
Principal investigator
🔴
Samir Baladi
Interdisciplinary AI Researcher — Theoretical Physics, Statistical Mechanics & Information Theory
Ronin Institute / Rite of Renaissance
Samir Baladi is an independent researcher affiliated with the Ronin Institute, developing the Rite of Renaissance interdisciplinary research program. ENTRO-QUANTUM is the seventh project (E-LAB-07) in a ten-project research program, building directly on ENTROPIA (E-LAB-01), ENTRO-AI (E-LAB-02), ENTRO-CORE (E-LAB-03), ENTRO-ENGINE (E-LAB-04), ENTRO-EVO (E-LAB-05) and ENTRO-NET (E-LAB-06).
No conflicts of interest declared. All code and data are open-source under MIT License.
📝 Citation
How to cite
@software{baladi2026entroquantum,
author = {Samir Baladi},
title = {ENTRO-QUANTUM: Entropic Collapse in Probabilistic State Spaces
of Artificial Intelligence},
year = {2026},
version = {1.0.0},
publisher = {Zenodo},
doi = {10.5281/zenodo.19478805},
url = {https://doi.org/10.5281/zenodo.19478805},
note = {E-LAB-07. Builds on E-LAB-01 through E-LAB-06}
}
@software{baladi2026entropia,
title = {ENTROPIA: Statistical Dynamics of Information Dissipation},
author = {Samir Baladi},
year = {2026},
doi = {10.5281/zenodo.19416737},
note = {E-LAB-01}
}
@software{baladi2026entroai,
author = {Samir Baladi},
title = {ENTRO-AI: Entropy-Resistant Inference Architecture},
year = {2026},
version = {2.0.0},
doi = {10.5281/zenodo.19284086},
note = {E-LAB-02}
}
@software{baladi2026entrocore,
author = {Samir Baladi},
title = {ENTRO-CORE: Self-Regulated Intelligence},
year = {2026},
version = {1.0.0},
doi = {10.5281/zenodo.19431029},
note = {E-LAB-03}
}
@software{baladi2026entroengine,
author = {Samir Baladi},
title = {ENTRO-ENGINE: Entropy Flow Regulator},
year = {2026},
version = {1.0.0},
doi = {10.5281/zenodo.19441032},
note = {E-LAB-04}
}
@software{baladi2026entrovevo,
author = {Samir Baladi},
title = {ENTRO-EVO: Adaptive Entropy Weighting for Self-Calibrating Systems},
year = {2026},
version = {1.0.0},
doi = {10.5281/zenodo.19464489},
note = {E-LAB-05}
}
@software{baladi2026entronet,
author = {Samir Baladi},
title = {ENTRO-NET: Distributed Entropy Synchronization Protocols},
year = {2026},
version = {1.0.0},
doi = {10.5281/zenodo.19474217},
note = {E-LAB-06}
}
"True intelligence is not the elimination of uncertainty — it is the art of acting optimally within it. ENTRO-QUANTUM gives intelligent systems the mathematical framework to embrace uncertainty as a resource."