Title: Correlation Matching for Constraint-Enhanced Physical Search

Abstract: Rather than simply introducing noise into search mechanisms, physical systems enforce constraints that produce structured correlations. This study introduces the concept of constraint-enhanced physical search, a framework where temporal correlations in the exploration phase are aligned with the spatial correlations induced by constraints in the update dynamics. Through the application of a minimal tug-of-war bandit model (TOW), we demonstrate that a conservation law transforms local observations into differential evidence among various options, while a temporally correlated drive dictates the sequence of exploration. Our findings indicate that search efficiency is optimized not through increased randomness or extreme anti-correlation, but by synchronizing temporal correlation with the physical update scale responsible for converting feedback into evidence. A scaling analysis reveals that the ratio of update noise to contrast serves as the primary parameter constraining the extent to which temporal anti-correlation can be effectively utilized. These results propose a broad organizing principle for physical search: structured spatiotemporal correlations arise from constraints and fluctuations, and optimal exploration is achieved when these correlations are matched to the underlying update dynamics.

Source: arXiv Generated at: 2026-06-04 00:00:00 UTC