We study experimentally and theoretically the optimal mean time needed by a free diffusing Brownian particle to reach a target at a distance $L$ from an initial position in the presence of resetting. Both the initial position and the resetting position are Gaussian distributed with width $\sigma$. We derived and tested two resetting protocols, one with a periodic and one with random (Poissonian) resetting times. We computed and measured the full first-passage probability distribution that displays spectacular spikes immediately after each resetting time for close targets. We study the optimal mean first-passage time as a function of the resetting period and rate for different values of the ratio $b=L/\sigma$ and find an interesting phase transition at a critical value $b=b_c$. For $b_c<b<\infty$, there is a metastable optimum time which disappears for $b<b_c$. The intrinsic difficulties in implementing these protocols in experiments are also discussed.

We introduce from an experimental point of view the main concepts of fluctuation theorems for work, heat and entropy production in out-of-equilibrium systems. We will discuss the important difference between the applications of these concepts to stochastic systems and to a second class of systems (chaotic systems) where the fluctuations are induced either by chaotic flows or by fluctuating driving forces. We will mainly analyze the stochastic systems using the measurements performed in two experiments: (a) a harmonic oscillator driven out of equilibrium by an external force; (b) a colloidal particle trapped in a time-dependent double-well potential. We will rapidly describe some consequences of fluctuation theorems and some useful applications to the analysis of experimental data. As an example, the case of a molecular motor will be analyzed in some detail. Finally we will discuss the problems related to the applications of fluctuation theorems to chaotic systems.

We experimentally, numerically and theoretically study the optimal mean time needed by a Brownian particle, freely diffusing either in one or two dimensions, to reach, within a tolerance radius R _tol , a target at a distance L from an initial position in the presence of resetting. The reset position is Gaussian distributed with width σ . We derived and tested two resetting protocols, one with a periodic and one with random (Poissonian) resetting times. We computed and measured the full first-passage probability distribution that displays spectacular spikes immediately after each resetting time for close targets. We study the optimal mean first-passage time as a function of the resetting period/rate for different target distances (values of the ratios b = L / σ ) and target size ( a = R _tol / L ). We find an interesting phase transition at a critical value of b , both in one and two dimensions. The details of the calculations as well as the experimental setup and limitations are discussed.

We study both experimentally and theoretically the statistical properties of the energy exchanged between two electrical conductors, kept at different temperatures by two different heat reservoirs, and coupled by the electrical thermal noise. Such a system is ruled by the same equations as two Brownian particles kept at different temperatures and coupled by an elastic force. We measure the heat flowing between the two reservoirs and the thermodynamic work done by one part of the system on the other. We show that these quantities exhibit a long-time fluctuation theorem. Furthermore, we evaluate the fluctuating entropy, which satisfies a conservation law. These experimental results are fully justified by the theoretical analysis. Our results give more insight into the energy transfer in the famous Feynman ratchet, widely studied theoretically but never in an experiment.

We provide a theoretical and experimental protocol that dynamically controls the effective temperature of a thermal bath, through a well-designed noise engineering. We use this powerful technique to shortcut the relaxation of an overdamped Brownian particle in a quadratic potential by a joint time engineering of the confinement strength and of the noise. For an optically trapped colloid, we report an equilibrium recovery time reduced by about two orders of magnitude compared to the natural relaxation time. Our scheme paves the way towards reservoir engineering in nanosystems.

An autonomous out-of-equilibrium Maxwell's demon is used to reverse the natural direction of the heat flux between two electric circuits kept at different temperatures and coupled by the electric thermal noise. The demon does not process any information, but it achieves its goal by using a frequency-dependent coupling with the two reservoirs of the system. There is no mean energy flux between the demon and the system, but the total entropy production $(\mathrm{system}+\mathrm{demon})$ is positive. The demon can be power supplied by thermocouples. The system and the demon are ruled by equations similar to those of two coupled Brownian particles and of the Brownian gyrator. Thus our results pave the way to the application of autonomous out-of-equilibrium Maxwell's demons to coupled nanosystems at different temperatures.