Nonclassical Heat Transfer and Recent Progress.

Heat transfer in solids has traditionally been described by Fourier's law, which assumes local equilibrium and a diffusive transport regime. However, advancements in nanotechnology and the development of novel materials have revealed non-classical heat transfer phenomena that extend beyond this traditional framework. These phenomena, which can be broadly categorized into those governed by kinetic theory and those extending beyond it, include ballistic transport, phonon hydrodynamics, coherent phonon transport, Anderson localization, and glass-like heat transfer. Recent theoretical and experimental studies have focused on characterizing these non-classical behaviors using methods such as the Boltzmann transport equation, molecular dynamics, and advanced spectroscopy techniques. In particular, the dual nature of phonons, exhibiting both particle-like and wave-like characteristics, is fundamental to understanding these phenomena. This review summarizes state-of-the-art findings in the field, highlighting the importance of integrating both particle and wave models to fully capture the complexities of heat transfer in modern materials. The emergence of new research areas, such as chiral and topological phonons, further underscores the potential for advancing phonon engineering. These developments open up exciting opportunities for designing materials with tailored thermal properties and new device mechanisms, potentially leading to applications in thermal management, energy technologies, and quantum science.