Diffusion driven by temperature or concentration gradients is a fundamental mechanism of energy and mass transport that inherently differs from wave propagation in both physical foundations and application prospects. Compared with conventional schemes, metamaterials provide an unprecedented potential for governing diffusion processes, based on emerging theories like the transformation and the scattering-cancellation theory that expanded the original concepts and suggested innovative metamaterial-based devices. The term diffusionics is used in the review to generalize these noteworthy achievements in various energy and mass diffusion systems. Examples include heat diffusion systems and particle and plasma diffusion systems. For clarity the numerous studies published over the past decade are categorized by diffusion field (i.e., heat, particles, and plasmas) and discussed from three different perspectives: the theoretical perspective, to detail how the transformation principle is applied to each diffusion field; the application perspective, to introduce various interesting metamaterial-based devices, such as cloaks and radiative coolers; and the physics perspective, to connect them with concepts of recent concern, such as non-Hermitian topology, nonreciprocal transport, and spatiotemporal modulation. The possibility of controlling diffusion processes beyond metamaterials is also discussed. Finally, several future directions for diffusion metamaterial research, including the integration of metamaterials with artificial intelligence and topology concepts, are examined.

• Received 15 February 2023

DOI:https://doi.org/10.1103/RevModPhys.96.015002