Heat flow that deviates from classical behavior in thin films or nanostructures under external fields.Anomalous heat transport refers to heat conduction that deviates from the classical Fourier law, where heat flow is proportional to the temperature gradient. In thin films, nanostructures, or under strong external fields, heat can flow in unexpected ways — sometimes even against the gradient, or with a dependence on system size that defies bulk behavior. This phenomenon is crucial for managing heat in nanoscale electronics, where conventional cooling fails, and for understanding energy transport in astrophysical plasmas and turbulent systems.
The deviation from Fourier's law in low-dimensional systems was predicted theoretically in the 1960s–1970s, but experimental confirmation came only in the 2000s with advances in nanofabrication and measurement techniques. The term 'anomalous' was borrowed from plasma physics, where it was used in the 1950s to describe unexpectedly fast heat loss in fusion devices.
Classical heat conduction assumes that heat carriers (electrons, phonons) scatter randomly, leading to a diffusive flow. In nanostructures, the mean free path of carriers can be comparable to or larger than the system size, so heat transport becomes ballistic or quasi-ballistic, leading to size-dependent thermal conductivity. Under external fields (like magnetic or electric), carriers can be deflected, causing anisotropic or even 'negative' heat flow — where heat moves from cold to hot — due to quantum interference or non-equilibrium effects. In turbulent plasmas, anomalous transport arises from chaotic magnetic field lines that allow heat to escape much faster than classical collisions would predict.
Anomalous heat transport is key to designing efficient thermoelectric devices, cooling computer chips, and predicting heat loss in fusion reactors (tokamaks), where it can limit performance.
In some 1D chains, heat conduction can be 'ballistic' — meaning it flows without any resistance, like light in a vacuum — even at finite temperatures, a phenomenon that has no analogue in 3D materials.








