Trajectory Functionals in the Thermodynamics of Radiation-Induced Damage in Structural Materials

This paper delivers a novel self-consistent non-local kinetic framework based on dose-dependent semi-Markov renewal transport and the generalized Doob's h-transform to evaluate the structural degradation of WWER-1000/1200 fuel claddings. By leveraging the Feynman-Kac formalism, we map the continuous microscopic defect path trajectories generated by the Liouville operator directly onto the evolution of the macroscopically integrated damage potential. The framework accounts for long-range memory effects in the degradation kinetics via a non-vanishing structural commutator of the path Liouville operator and Zwanzig-Mori projection operators, which mathematically links the spatial restrictions of microscopic sinks to energetic path penalties. Spatial profiling of the cladding's mean lifetime, demonstrates a distinct sigmoidal, S-shaped degradation trajectory encompassing distinct incubation, linear growth, and avalanche breakdown stages. The numerical results reveal an abrupt, localized reduction in the operational lifespan near the cladding boundaries. This marginal vulnerability is shown to be a direct physical consequence of boundary stress field singularities at the fuel cladding interface and localized embrittlement. The developed path integral architecture provides a strict thermodynamic link between non-equilibrium fluctuations and the global Griffiths macro-barrier, offering a robust predictive tool for high-burnup nuclear fuel safety assessments.