Abstract
The untapped potential of thermal metamaterials requires the simultaneous observation of both diffusive and wave-like heat propagation across multiple length scales that can only be realised through theories beyond Fourier. Here, we demonstrate that tailored material patterning significantly modifies heat transport dynamics with enhanced non-Fourier behaviour, effectively trapping heat (temporarily). By bridging phonon scattering mechanisms with macroscopic heat flux via a novel perturbation-theory approach, we derive the hyperbolic Cattaneo model directly from particle dynamics, establishing a direct link between relaxation time and phonon lifetimes. Our micro-scale patterned systems exhibit extended non-Fourier characteristics, where internal interfaces mediate wave-like energy propagation, diverging sharply from diffusive Fourier predictions. These results provide a unified framework connecting micro-scale interactions to macroscopic transport, resolving long-standing limitations of the Cattaneo model. This work underscores the transformative potential of thermal metamaterials for ultra-fast thermal management and nanoscale energy applications, laying a theoretical foundation for next-generation thermal technologies.