New Theory Unifies Heat's Memory and Nonlocal Transport
Physicists Jianjun Dong and Yi Zeng have developed a unified theoretical framework that describes heat conduction as a process with memory and spatial
A new theoretical framework developed by physicists at Auburn University provides a unified description of heat conduction that accounts for memory and spatial nonlocality, phenomena that become significant at microscopic scales and ultrafast times. The work, led by Jianjun "JJ"Dong, the Thomas and Jean Walter Professor in the Department of Physics, and Auburn alumnus Yi Zeng, was published in the journal Physical Review B."Heat does not remember in the way that we remember a person or an event," Dong said. "Its memory is stored in the microscopic motion of the material. The heat flowing at this moment can still carry information about a temperature disturbance that occurred earlier." At the scale of modern computer chips or over trillionths of a second, heat flow can retain the influence of past disturbances and extend its effect over distance, a departure from the "here and now" assumption of Fourier's law.
When the Textbook Rule Begins to Bend
For centuries, Fourier's law has successfully described heat conduction in everyday objects, assuming an immediate, local response. However, in crystalline solids where heat is carried by phonons-collective atomic vibrations-this description breaks down at very small length scales and short times. Some phonons travel significant distances before scattering, causing heat transport to appear diffusive, quasi-ballistic, spatially nonlocal, or even wave-like. Scientists have typically used separate models for these different regimes. The new framework unifies them within a single mathematical description.
"Instead of choosing a different theory every time heat begins to behave differently, we wanted to identify the deeper microscopic structure connecting those behaviors,"Zeng explained. In their framework, familiar behaviors like diffusion and hydrodynamic transport emerge as different limits of the same underlying theory."Thermal conductivity is an extremely useful number, but a single number cannot always tell the full story," Dong noted. "At very small length scales and very short times, we need to know how far the thermal response extends and how long its influence persists." The kernel is derived from statistical mechanics, connecting it to equilibrium fluctuations of heat flow, thereby generalizing the foundational Green-Kubo relation.
Silicon Remembers-But Distance Matters More
The researchers demonstrated their framework by constructing the kernel for crystalline silicon at room temperature and modeling transient thermal grating experiments. These experiments use laser pulses to create temporary temperature patterns, observing their decay across spatial periods from tens of micrometers down to nanometers.
The calculations revealed that, under the studied conditions, the dominant departure from Fourier behavior came from spatial nonlocality-the reach of the heat flow response-rather than from temporal memory alone. Silicon contains phonons with a broad range of mean free paths. At small scales, phonons with long mean free paths cannot be treated as transferring energy only locally. Temporal memory was strongest during the earliest stages of the thermal response. The full framework reproduced the transition away from conventional diffusion across multiple length scales and, when accounting for boundary scattering in a thin silicon membrane, agreed quantitatively with published experimental data.
Not Every Heat Wave Tells the Same Story
The theory also clarifies the interpretation of wave-like temperature propagation, which can occur under certain conditions. It shows that such wave-like responses are specific limits of the more general nonlocal, memory-carrying transport described by the unified framework, rather than fundamentally separate phenomena.
