Testable Deviations from the Born Rule Induced by Modular Nonequilibrium

ina The Born rule is a cornerstone of quantum mechanics, yet it is introduced as a postulate rather than derived from underlying dynamics. Here we show that Born probabilities arise as an equilibrium condition associated with modular (KMS) balance in quantum systems. When this balance is weakly violated, we predict small but controlled deviations from the Born rule governed by mod- ular nonequilibrium and entropy production. We derive a universal first-order correction to measurement probabilities that vanishes exactly at equilibrium while preserving normalization. Importantly, we identify experimentally ac- cessible non-KMS protocols in current quantum platforms where the predicted deviations can be statistically detected as a purely statistical bias in large-N data (and is invisible at the level of individual events). We further show that the correction is compatible with relativistic causality: for bipartite systems it depends only on local modular data of the measured subsystem and therefore does not enable superluminal signalling. Our results provide a falsifiable test of the dynamical origin of quantum probabilities beyond the standard postulate.