Born's rule deviations from temporal non-local effects

Abstract: We investigate deviations from Born's rule in quantum systems where the quantum-equilibrium hypothesis, $\rho \neq |\Psi|^2$, fails. Using the quantum-hydrodynamic framework, we show that transit-interference phenomena and intrinsic memory effects induce finite-time non-local correlations, resulting in violations of Born's rule. These effects appear as non-exponential decay in the survival probability of unstable states at intermediate timescales. Our findings challenge conventional interpretations of quantum probability and suggest novel dynamics that could guide future experimental investigations of temporal non-locality.