When heat flows like water
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EPFL researchers have shown theoretically that, in highly ordered materials, heat can flow toward warmer regions without violating the laws of thermodynamics. Their work could help design electronics that minimize heat loss.
To understand how heat normally flows, you could study the second law of thermodynamics – or wrap your hands around a hot mug of coffee. Both tell us that heat tends to flow toward cooler regions. As a material’s thermal energy increases, its atoms vibrate, and quantum mechanics describes these vibrations as phonons: quasiparticles that transport heat. Normally, collisions between phonons cause heat to dissipate slowly. But in highly ordered, pure crystals, these collisions can result in a fluid-like, directional heat flow known as phonon hydrodynamics.
Researchers from the group of Theory and Simulation of Materials, led by Nicola Marzari, in EPFL’s School of Engineering have demonstrated theoretically that hydrodynamic heat flow can cause heat to swirl into vortices, and even move from cooler regions back toward warmer ones. Using simulations, they show how to maximize hydrodynamic heat flow in a 2D strip of crystalline graphite. In addition to revealing the underlying physics of this phenomenon for the first time, their analytical model offers a powerful tool for harnessing heat ‘backflow’ to manage thermal energy in electronic devices.
Our approach will allow us to guide experimentalists in developing electronic devices that leverage this effect to manage heat more efficiently.
First author Enrico Di Lucente
“Previous work relied on numerical modelling, which describes temperature patterns but doesn’t fully explain how physical quantities influence each other,” explains first author and former EPFL researcher Enrico Di Lucente, now a postdoc at Columbia University. “Thanks to our analytical framework, we have shown that heat backflow is maximized when the flow is nearly incompressible. Our approach will allow us to guide experimentalists in developing electronic devices that leverage this effect to manage heat more efficiently.
The researchers say their work, recently published in Physical Review Letters, could impact heat management across multiple sectors, ranging from consumer electronics and industry to energy storage, data centers, and cloud computing.
A path to cooler, faster electronics
Although experimental evidence of phonon hydrodynamics dates back to the 1960s, researchers have lacked the fundamental theoretical understanding required to fully exploit the fluid-like nature of hydrodynamic heat flow.
The EPFL team’s analytical framework reveals that the temperature profile of a hydrodynamic system can be broken down into vorticity (how heat flow swirls) and compressibility (how it is squeezed). This explains why heat backflow is maximized when compressibility is minimized: when heat flow is incompressible, it cannot be squeezed or bunched up when it encounters resistance but is instead redirected backward. This localized reversal enables more efficient, coordinated flow by reducing heat buildup, which can lead to overheating and impaired performance in electronic devices.
“In hydrodynamic heat backflow, heat flows from cooler regions to warmer ones, leading to a negative temperature difference and overall negative thermal resistance across the device,” Di Lucente says. “This effect is very small, but now we can design experiments to maximize it, potentially changing how we think about energy loss in electronic systems. For example, you could imagine a smartphone with a hydrodynamic component to direct thermal energy away from the battery, so it doesn’t overheat.”
Marzari emphasizes that the formulations can be used to study any other microscopic carrier, from electrons to more complex quantum particles, and that the ease with which these carriers travel can be calculated directly from quantum mechanics’ fundamental equations (first principles).
“In addition to this impactful theoretical development, our first-principles simulations provide a realistic description of physical systems quickly and inexpensively compared to the cost of building new experimental setups. At the same time, they can indicate where experimental efforts should be focused to develop more heat-efficient electronics,” he says. cost of building new experimental setups. At the same time, they can indicate where experimental efforts should be focused to develop more heat-efficient electronics,” he says.
References
Di Lucente, E., Libbi, F., Marzari, N. et al. Vortices and Backflow in Hydrodynamic Heat Transport. Phys. Rev. Lett. (2026) https://journals.aps.org/prl/abstract/10.1103/g9dx-hjyn
Simoncelli, M., Marzari, N., Cepellotti, A. Generalization of Fourier’s Law into Viscous Heat Equations. Phys. Rev. X. (2020) https://journals.aps.org/prx/abstract/10.1103/PhysRevX.10.011019
Source: EPFL
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