Rare-Event Fidelity in Simulated Thermodynamic Samplers

Abstract

Thermodynamic computing aims to reduce the cost of sampling by drawing on the natural fluctuations of physical systems. Realizing this promise requires understanding how the probabilities generated by a sampling process relate to those of the intended model, especially for rare events. We present a computational reference study of rare-event fidelity in simulated thermodynamic samplers. Combining a fixed GPU experiment with exploratory mathematical analysis, we calculate ideal stationary-law references for 133 of 140 conditions and examine how update rules, finite runtime, and diagnostic approval shape reported event probabilities. The resulting cases show how precise, repeatable estimates can describe an altered sampling distribution while missing the intended event probability. Finite-run calculations reveal how transient behavior can mask stationary bias, while independent-sampling calculations show how count-based selection can favor upward fluctuations and reduce interval coverage among approved estimates. These findings motivate evaluating the sampled distribution, the information in a finite run, and the effects of diagnostic selection separately. The accompanying reference probabilities and calculations provide test cases for future evaluation of probabilistic algorithms and thermodynamic hardware. This release contains the white paper, its narrated audio edition, and supporting evidence: derived records for 35,840 replicates across 140 conditions, scientific registries, mathematical reference tables, selected analysis scripts, and provenance. The evidence bundle documents its reproduction scope; it does not contain the complete raw-chain archive. The exploratory analyses were conducted after the fixed GPU experiment. The study reports software simulations and mathematical calculations, not measurements of physical thermodynamic hardware. The original study registration is available at https://osf.io/e637g/. The paper documents deviations from the registered analysis and distinguishes the executed experiment from subsequent exploratory work. Farynth self-funded the study and ran it on company-owned hardware.