Linking fluctuation and dissipation in spatially extended out-of-equilibrium systems

TL;DR

This paper extends the fluctuation-dissipation theorem to out-of-equilibrium systems, demonstrating experimentally that thermal noise in a heated microcantilever can be predicted from local dissipation measurements.

Contribution

It introduces a novel approach linking fluctuations and dissipation in out-of-equilibrium spatially extended systems, validated through experiments on microcantilevers with different damping profiles.

Findings

Thermal noise correlates with local energy dissipation.

Thermal profile influences fluctuation amplitude.

Fluctuations can be predicted from dissipation measurements.

Abstract

For systems in equilibrium at a temperature $T$, thermal noise and energy damping are related to $T$ through the fluctuation-dissipation theorem (FDT). We study here an extension of the FDT to an out of equilibrium steady state: a microcantilever subject to a constant heat flux. The resulting thermal profile in this spatially extended system interplays with the local energy dissipation field to prescribe the amplitude of mechanical fluctuations. Using three samples with different damping profiles (localized or distributed), we probe this approach and experimentally demonstrate the link between fluctuations and dissipation. The thermal noise can therefore be predicted a priori from the measurement of the dissipation as a function of the maximum temperature of the micro-oscillator.