## Final Report Summary - OUTEFLUCOP (Out of Equilibrium Fluctuations in Confined Phase Transitions)

The main goal of this project was the study of out-of equilibrium fluctuations in confined liquid and phase transitions. The following three main questions have been analyzed: i) Role of confinement on the statistical properties of fluctuations.ii) The fluctuations of the injected and dissipated power in systems driven out of equilibrium ;iii) The relevance of fluctuations for applications.

The local measurements and the confinement are realized using original ultra low noise force and displacement measurements developed in our laboratory, which make use of optical tweezers and cantilevers.. Technical improvements have been designed in order to reduce spurious effects, which may perturb the main phenomena that we want to investigate.

These apparatuses have been applied to the study of the above mentioned main goals of this project, getting the following important results: 1) the study of the Transient Fluctuation Dissipation Theorem after a quench to a critical point 2) the observation(both theoretically and experimentally ) of an oscillating phase transition induced by a localized constant perturbation 3) The experimental characterization of a critical Casimir induced synchronization of the motion of Brownian particles. This result, which is exactly on the line of the 3 originally proposed topics, opens many interesting perspectives on transient Casimir and addictivity on which we are still working. 4) The first direct numerical simulation of the critical Casimir forces in a binary mixture of two kind of particles coupled by Lenard-Jones potentials. This result shows for the first time the existence of a pressure anisotropy that in principle could be experimentally detectable. This numerical simulation opens the way to the study of time dependent critical Casimir forces. 5) Viscous flows around nanowires.

These achievements came together with several results that are products and interdisciplinary developments of OUTEFLUCOP.

1) Stochastic thermodynamics

Besides these results, several experiments on stochastic thermodynamics connected with Outeflucop have been developed. We worked on the stochastic heat transfer between two viscously coupled Brownian particles kept at different different temperatures. A Fluctuation Theorem has been derived for the heat flux induced by the viscous coupling [9, 10]. We use the results of these experiments for testing an out of equilibrium Fluctuation Dissipation Theorem, useful to compute the response to a temperature variation of a system submitted to a temperature difference. Finally we studied the stochastic properties of work in a periodically driven electric circuit.

1) outof equilibrium fluctuations, information theory and stochastic thermodynamics

In 2012 we got a very interesting result by measuring for the first time the amount of energy necessary to erase a bit of information. Within this context we have shown both experimentally and theoretically the connection between the generalized Jarzynski equality ( a key relation in stochastic thermodynamics) and the Landauer’s bound. This research on information and thermodynamics connections is in full development for the important consequences that it might have both for computation and for feedback control based on Maxwell demon.

2) Engineered Swift Equilibration (ESE)

Motivated by our measurements on stochastic thermodynamics we looked for an optimization process which allow a system to relax to a new equilibrium position much faster than its relaxation time. To do that we designed a protocol, named Engineered Swift Equilibration (ESE), that shortcuts timeconsuming relaxations. We implement the process experimentally (on Brownian particles and AFM cantilevers) showing that it allows the system to reach equilibrium 100 times faster than the naturalequilibration rate. The method paves the way for applications in micro- and nano-devices,where the reduction of operation time represents as substantial a challenge as miniaturization.

The local measurements and the confinement are realized using original ultra low noise force and displacement measurements developed in our laboratory, which make use of optical tweezers and cantilevers.. Technical improvements have been designed in order to reduce spurious effects, which may perturb the main phenomena that we want to investigate.

These apparatuses have been applied to the study of the above mentioned main goals of this project, getting the following important results: 1) the study of the Transient Fluctuation Dissipation Theorem after a quench to a critical point 2) the observation(both theoretically and experimentally ) of an oscillating phase transition induced by a localized constant perturbation 3) The experimental characterization of a critical Casimir induced synchronization of the motion of Brownian particles. This result, which is exactly on the line of the 3 originally proposed topics, opens many interesting perspectives on transient Casimir and addictivity on which we are still working. 4) The first direct numerical simulation of the critical Casimir forces in a binary mixture of two kind of particles coupled by Lenard-Jones potentials. This result shows for the first time the existence of a pressure anisotropy that in principle could be experimentally detectable. This numerical simulation opens the way to the study of time dependent critical Casimir forces. 5) Viscous flows around nanowires.

These achievements came together with several results that are products and interdisciplinary developments of OUTEFLUCOP.

1) Stochastic thermodynamics

Besides these results, several experiments on stochastic thermodynamics connected with Outeflucop have been developed. We worked on the stochastic heat transfer between two viscously coupled Brownian particles kept at different different temperatures. A Fluctuation Theorem has been derived for the heat flux induced by the viscous coupling [9, 10]. We use the results of these experiments for testing an out of equilibrium Fluctuation Dissipation Theorem, useful to compute the response to a temperature variation of a system submitted to a temperature difference. Finally we studied the stochastic properties of work in a periodically driven electric circuit.

1) outof equilibrium fluctuations, information theory and stochastic thermodynamics

In 2012 we got a very interesting result by measuring for the first time the amount of energy necessary to erase a bit of information. Within this context we have shown both experimentally and theoretically the connection between the generalized Jarzynski equality ( a key relation in stochastic thermodynamics) and the Landauer’s bound. This research on information and thermodynamics connections is in full development for the important consequences that it might have both for computation and for feedback control based on Maxwell demon.

2) Engineered Swift Equilibration (ESE)

Motivated by our measurements on stochastic thermodynamics we looked for an optimization process which allow a system to relax to a new equilibrium position much faster than its relaxation time. To do that we designed a protocol, named Engineered Swift Equilibration (ESE), that shortcuts timeconsuming relaxations. We implement the process experimentally (on Brownian particles and AFM cantilevers) showing that it allows the system to reach equilibrium 100 times faster than the naturalequilibration rate. The method paves the way for applications in micro- and nano-devices,where the reduction of operation time represents as substantial a challenge as miniaturization.