Unified Statistical Theory of Heat Conduction in Nonuniform Media
This paper presents a unified statistical theory of heat conduction in nonuniform media by deriving a causal spatiotemporal kernel via the Zwanzig projection-operator formalism, which microscopically encodes memory, nonlocality, and heterogeneity to seamlessly bridge classical diffusion, hydrodynamic, and quasi-ballistic transport regimes while recovering conventional coefficients as coarse-grained limits.