Alex Fontana, , PhD Thesis, Université de Lyon (2020)
hal: tel-03325266
The goal of this thesis is a theoretical and experimental study of the non-equilibrium prop- erties of thermal noise, with the purpose of understanding whether we can extend certain statistical physics tools to non-equilibrium systems. In particular, we show how we can ex- tend the Fluctuation-Dissipation Theorem (FDT) to systems subjected to a stationary spatial temperature profile, thus in a Non-Equilibrium Steady State (NESS). Since thermal fluctua- tions cannot be described by a single temperature through the Equipartition Theorem, we show how they are then prescribed by the temperature profile weighted by the local me- chanical dissipation.
We test this prediction in various silicon micro-cantilevers, creating a strong temperature difference of hundreds of degrees between the base and the tip. In one experiment in par- ticular, the base is held at cryogenic temperatures, thus placing the cantilever as far from equilibrium as physically possible. We then measure the thermal fluctuations of the sample alongside their dissipation, showing how these two quantities are perfectly construed by our theoretical framework. The same is also verified for a macroscopic aluminum oscillator. A careful analysis of the statistical properties of thermal noise finally demonstrates that our results are robust, and a sorting algorithm of the experimental data is proposed. A simple method to estimate the uncertainties of the measurements is finally given.