A microscopic time-domain theory of transient heat conduction built on Zwanzig's statistical theory of irreversible processes. The central time-domain transport function Z(t), defined through equilibrium heat-flux time-correlation functions, generalizes steady-state thermal conductivity into a memory function that governs the crossover from finite-speed second-sound wave propagation to diffusion. It captures intrinsic memory effects without mesoscopic constructs, applies to any temperature or length scale, and links first-principles atomistic input to continuum transport for transient-thermal-grating experiments.
Ultrafast and nanoscale heat transport violates Fourier's law — heat can propagate as a wave (second sound) at finite speed before settling into ordinary diffusion — but existing generalizations of F…