Q-Bond Landauer–Nelson–TICE Bridge

Author: Kevin Henry Miller — Founder & President, Q-Bond Network DeSCI DAO, LLC
Email: Kevin@qbondnetwork.com
ORCID: 0009-0007-7286-3373

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Core Result

$$E_{\text{bridge}} = k_B T \ln!\left(\frac{2k_B T}{\gamma\hbar}\right)$$

and

$$E_{\text{bridge}} = k_B T \ln 2 \quad\iff\quad \gamma = \frac{k_B T}{\hbar}$$

Five conditions — on the diffusion ratio, friction, correlation time, bridge energy, and temperature independence — are proven pairwise equivalent. Under a single closure postulate ($D_{\text{th}} = 2D_q$), the bridge energy equals exactly one Landauer bit of erasure.

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What This Repository Contains

Folder	Contents
paper/	Manuscript PDF, supplement PDF, LaTeX sources, bibliography, figures
src/bt11/	Reusable Python modules: bridge energy, kernels, inversions, constants
scripts/	Top-level reproducibility scripts
tests/	Verified test suite (28+ checks, all PASS)
results/	Pre-generated tables, figures, verification summary
docs/	Theorem statement, assumptions, referee notes

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What Is Proved

• Exact diffusion-ratio identity: $R = D_{\text{th}}/D_q = 2k_BT/(\gamma\hbar)$
• Five-way equivalence theorem (conditions i–v, pairwise)
• Exact deviation formula: $\Delta E = -k_BT\ln(1+\delta)$
• TICE closure factor: $C_{\text{TICE}}(t) = k_BT/[\hbar\gamma_{\text{eff}}(t)]$
• Three kernel solutions (Ohmic–Drude, algebraic, Gaussian) with crossing times
• Mass independence of the bridge energy
• Second-law consistency of the deviation sign

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What Is Not Proved

• Conjecture 1 ($D_{\text{th}} = 2D_q$) is a closure postulate, not derived from first principles.
• Bochner positivity guarantees kernel admissibility, not uniqueness.
• This is a conditional theorem, not an unconditional derivation of Landauer from Nelson stochastic mechanics.

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Reproduce

# Clone
git clone https://github.com/quantumblackswan/qbond-landauer-nelson-bridge.git
cd qbond-landauer-nelson-bridge

# Install
pip install -r requirements.txt

# Run full verification (28 checks)
python scripts/landauer_nelson_solved.py

# Reproduce figures
python scripts/reproduce_figures.py

# Run test suite
pytest tests/ -v

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Citation

See CITATION.cff or click "Cite this repository" on GitHub.

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License

MIT