Abstract
We develop an entropic extension of the Heisenberg uncertainty principle that unifies spatial and temporal domains through a covariant tensor linking structural and optical entropy. Structural entropy quantifies spatial configuration derived from lattice constants, while optical entropy represents temporal dispersion extracted from emission spectra. As a proof of concept, the framework is applied to reactor pressure vessel (RPV) steels under neutron irradiation. The derived nonlinear entropy-stress relation reproduces the three experimental hardening regimes-linear, plateau, and exponential-observed over an 80-year operational lifespan. Agreement with ASTM E900 datasets confirms the predictive capacity of the model. By anchoring uncertainty in measurable quantities, this framework bridges quantum-like information limits and macroscopic material degradation, offering a general route for entropy-based prediction in engineering systems.