Reproducibility Package: A Nondimensional Langevin Model for Driven Stochastic Computing

Abstract

NTC-1 Reproducibility Package Nondimensional Driven Langevin Transport Model This repository contains Python source code, processed simulation outputs, configuration files, and figure-generation scripts supporting the revised manuscript: A Nondimensional Langevin Model for Driven Stochastic Computing: Conceptual Phononic and Isotopic Design Considerations The repository implements a one-dimensional nondimensional overdamped Langevin model in a bistable potential with a prescribed asymmetric drive. The stochastic equation is integrated with the Euler-Maruyama method. This is a theoretical and computational proof-of-concept. It does not report a fabricated device, experimentally measured coherence time, physical switching energy, experimentally calibrated electromagnetic coupling, phonon transport, implantation physics, or thermodynamic work extraction. Model The simulated state coordinate follows: dxt = μ[-∂xU(xt) + fdrv(xt)]dt + √(2μTeff) dWt with U(x) = J4x4 + J2x2 and prescribed drive: fdrv(x) = λα exp(-x2) All reported quantities are nondimensional unless explicitly stated otherwise. Reported Conditions The reproducibility workflow evaluates three prespecified model conditions: Condition Teff λα Purpose Deterministic reference 0.0 0.0 Noise-free numerical reference Undriven stochastic reference 0.8 0.0 Stochastic reference without prescribed asymmetric drive Driven stochastic condition 0.8 3.0 Stochastic condition with prescribed asymmetric drive For drive-amplitude sensitivity analyses: λα ∈ {0, 1, 2, 3, 4}. Main Reported Result For the stated parameterization and fixed nondimensional horizon tmax = 20, the observed barrier-crossing fraction was: 23.4% for the undriven stochastic reference; 62.0% for the driven condition at λα = 3.0. This is a model-conditioned transport result. It is not interpreted as a device-level speed, throughput, energy-efficiency, heat, entropy-production, or work-extraction measurement. Boundary Generativity Test (BGT) The Boundary Generativity Test (BGT) is included as an exploratory, model-evaluation reporting protocol. In this release, the implemented analysis reports: Distributional summaries of a defined one-step coordinate-increment observable; Conditional first-passage-time summaries; Barrier-crossing fractions; Drive-amplitude sensitivity; Time-step sensitivity. The BGT is not presented as a standardized or externally validated benchmark of physical generativity, thermodynamic work extraction, or hardware advantage. Formal Kolmogorov complexity and finite-sequence compression metrics are not evaluated in the present release. The code structure is intended to support future prespecified compressibility analyses when the encoding, quantization, trace length, preprocessing, estimator, software version, and uncertainty method are documented. System Requirements The workflow was developed for Python 3.8 or later. Required packages: numpy pandas scipy matplotlib Install dependencies with: pip install numpy pandas scipy matplotlib Reproducing the Analysis From the repository root, run: python reproduce_all.py The master script will: Run 30 independent seed-level batches of 1,000 trajectories per condition. Generate deterministic, undriven stochastic, and driven trajectory outputs. Pool the specified trajectories for ensemble visualizations. Compute batch-level first-passage summaries, crossing fractions, state-increment statistics, drive-amplitude sensitivity, and time-step sensitivity. Calculate reported uncertainty intervals from the 30 independent batch estimates using the method documented in the source code and manuscript. Export processed data to CSV files. Generate publication-ready PDF and PNG figures. Statistical Conventions The primary inferential unit is the independent simulation batch. Each reported condition uses 30 independent batches of 1,000 trajectories. First-passage times are conditional on crossing the threshold x ≥ b by the stated simulation horizon. Noncrossing trajectories are retained in crossing-fraction calculations and excluded from conditional first-passage-time distributions. The one-step coordinate-increment observable is Δxn = xn+1 - xn. Increment skewness and ordinary kurtosis are calculated separately for each independent batch before aggregation. The code does not label coordinate increments as physical heat, work, dissipation, entropy production, or switching energy. Repository Structure ntc1_reproducibility_v2/ ├── reproduce_all.py ├── README.md ├── requirements.txt ├── config/ │ ├── parameters.yaml │ └── random_seeds.csv ├── data/ │ ├── processed/ │ └── derived/ ├── results/ │ └── convergence_table.csv └── figures/ └── publication/ ├── Fig1_ConceptualArchitecture.pdf ├── Fig2_PotentialAndDrive.pdf ├── Fig3_Trajectories.pdf ├── Fig4_Observable.pdf ├── Fig5_FPT.pdf └── Fig6_Sensitivity.pdf Scope and Limitations The conceptual phononic, isotope-modified, CsPbBr3, and hBN architecture is not fabricated or experimentally validated in this repository. The present code does not simulate: Electromagnetic field distributions; Phononic band structures or phonon transport; Isotope-selective implantation, damage, or annealing; Interface chemistry or spin-relaxation pathways; Physical thermomechanical reliability; Calibrated optical, electrical, or thermal driving; Physical energy accounting or thermodynamic work extraction. Prospective NTC-2 Direction A future NTC-2 research direction could investigate whether integrated photonic or electro-optic structures, including silicon micro-ring resonators, can provide a physically calibrated asymmetric drive to an analogous stochastic transport element. Such an implementation would require a separately specified optical field model, device geometry, material-response model, energy accounting, and experimental validation; it is not evaluated in the present study. License Code is released under the MIT License. Copyright © 2026 Kevin Thorsen Baird and The C4 Institute.