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Physicists explain why unexpectedly small temperature fluctuations occur in objects exposed to extreme heat

06 Jul 2021
ENS de Lyon researchers
Hot and cold: members of the ENS de Lyon team adjusting their silicon cantilever experiment. (Courtesy: L Bellon/ENS de Lyon)

A new explanation for why thermal systems subjected to extreme heat fluxes display far lower temperature fluctuations than expected has been developed by researchers in France. By adding two additional components to a widely-used theorem for predicting fluctuations, Alex Fontana, and colleagues at ENS de Lyon have explained a key discrepancy between theory and experimental observations of silicon cantilevers exposed to extreme temperature gradients. Their discovery could improve high-precision experiments and the design of tiny machines.

As physical systems exchange heat with their surrounding environments, their temperatures will naturally fluctuate over time. These variations may be minuscule, but they can have a significant impact on the operation of microscale mechanical devices and the outcome of high-precision experiments. This has created a practical need to predict the extent of thermal fluctuations in different environments. To do this, physicists use a powerful tool called fluctuation-dissipation theorem (FDT).

Currently, it is often assumed that systems are in thermal equilibrium with their environments – absorbing exactly as much heat as they emit. Instead, out-of-equilibrium heat fluxes are common in many systems including living tissues and aging materials. According to the FDT, such systems should undergo higher temperature fluctuations than those in equilibrium. Yet in recent experiments, involving silicon cantilevers exposed to high temperature gradients, the mechanical vibrations induced by temperature fluctuations were far lower than the FDT predicted.

Extreme temperature gradient

In their study, Fontana’s team took the cantilever experiment to its extreme by cooling one end of a cantilever to cryogenic temperatures, while heating the other to just below its melting point. This induced a temperature gradient of 1700 K – the highest possible difference the system could sustain in a vacuum. The researchers discovered that while the amplitude of the vibrations did increase with the temperature gradient, they were far lower than the FDT predicted, given the average temperature of the system.

Fontana and colleagues successfully accounted for this discrepancy by introducing a simple extension to the FDT, containing two key aspects of mechanical dissipation. First, a “clamping loss” describes the mechanical energy lost at the cantilever’s base; and second, “distributed damping” accounted for the energy lost due to defects in the atomic structure of silicon along the length of the cantilever.

The team now hopes that by generalizing the FDT in this way for high heat fluxes, improvements could be made across a wide array of areas in research and engineering.

Better predictions could enable researchers to better describe the interaction between electromagnetic fields and living tissues; and improve the sensitivity of microelectromechanical devices. Elsewhere, they may even improve the resolution of the interferometers used in ground-based gravitational wave detectors – helping astronomers to better link atomic-scale detector movements to ripples in space–time.

The research is described in Physical Review E.

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