A simple proof of the Jarzynski equality?

In this short communication, I give a very simple derivation of the Jarzynski equality, which allows to compute the free energy difference of a body, which is driven between two equilibrium states $A$ and $B$ by an external (time-dependent) force, from the probability distribution function of the work done on the system, regardless of the nature of the transformation (reversible or irreversible) between the states $A$ and $B$. It perhaps throws some light on the debate recently started by Cohen and coworkers , and perhaps explains why all the experiments which has been performed in order to test the Jarzynski equality are successful, even in very defavorable (irreversible) cases (and more strikingly, when the state $B$ is not an equilibrium one)

Experimental study of work fluctuations in a harmonic oscillator

The work fluctuations of a harmonic oscillator in contact with a thermostat and driven out of equilibrium by an external force are studied experimentally. For the work both the transient and stationary state fluctuation theorems hold. The finite time corrections are very different from those of a first order Langevin equation. The heat and work fluctuations are studied when a periodic forcing is applied to the oscillator. The importance of the choice of the ''good work'' to compute the free energy from the Jarzinsky equality is discussed

Experimental study of work fluctuations in a harmonic oscillator

International audienceThe work fluctuations of a harmonic oscillator in contact with a thermostat and driven out of equilibrium by an external force are studied experimentally. For the work both the transient and stationary state fluctuation theorems hold. The finite time corrections are very different from those of a first order Langevin equation. The heat and work fluctuations are studied when a periodic forcing is applied to the oscillator. The importance of the choice of the ''good work'' to compute the free energy from the Jarzinsky equality is discussed

Fluctuations du travail et de la chaleur dans des systèmes mécaniques hors d'équilibre

Numéro d'ordre: 339Numéro attribué par la bibliothèque: 05ENSL0 339This thesis presents an experimental study of work and heat fluctuations of mechanical systems driven out of equilibrium. The aim is to test recent theoretical approaches mainly due to Jarzynski, Crooks, Gallavotti, Cohen, van Zon and coworkers. In a first chapter, we introduce these new results and motivate the need for performing experiments to test them. The second chapter is dedicated to the principles and to the experimental apparatus and device: a differential interferometer, inspired from the Nomarski technique, allows us to measure the thermal sub-nanometric displacements of mechanical dissipative oscillators. A third chapter is dedicated to the principle and to the setup of a new denoising technique inspired from Wiener's filtering. This technique allows us to strongly reduce the environmental noise transmitted to the experimental systems of interest. In the last two chapters, we experimentally and theoretically study work and heat production thermal fluctuations of small mechanical dissipative oscillators driven out of equilibrium.Ce travail propose une étude expérimentale au niveau fondamental des fluctuations du travail et de la chaleur dans des sytèmes mécaniques hors d'équilibre, en vue de valider les approches théoriques récentes sur le sujet dues à Jarzynski, Crooks, Gallavotti, Cohen, van Zon et leurs collaborateurs. Dans un premier chapitre, nous introduisons ces nouveaux concepts et motivons la nécessité de réaliser des expériences afin de tester ces nouveaux résultats. Le second chapitre est consacré aux principes ainsi qu'à la réalisation du dispositif de mesure: un interféromètre différentiel inspiré de la technique de Nomarski, permettant de mesurer les déplacements thermiques sub-nanométriques de petits oscillateurs mécaniques dissipatifs. Un troisième chapitre détaille le principe ainsi que la réalisation d'une technique de réduction du bruit originale s'inspirant du filtrage de Wiener, dans le but de s'affranchir du bruit environnemental transmis aux systèmes considérés. Dans les deux derniers chapitres, nous étudions expérimentalement et théoriquement les fluctuations du travail ainsi que de la production de chaleur de petits oscillateurs mécaniques dissipatifs portés dans des états hors d'équilibre

Fluctuations du travail et de la chaleur dans des systèmes mécaniques hors d'équilibre

Ce travail propose une étude expérimentale au niveau fondamental des fluctuations du travail et de la chaleur dans des sytèmes mécaniques hors d'équilibre, en vue de valider les approches théoriques récentes sur le sujet dues à Jarzynski, Crooks, Gallavotti, Cohen, van Zon et leurs collaborateurs. Dans un premier chapitre, nous introduisons ces nouveaux concepts et motivons la nécessité de réaliser des expériences afin de tester ces nouveaux résultats. Le second chapitre est consacré aux principes ainsi qu'à la réalisation du dispositif de mesure: un interféromètre différentiel inspiré de la technique de Nomarski, permettant de mesurer les déplacements thermiques sub-nanométriques de petits oscillateurs mécaniques dissipatifs. Un troisième chapitre détaille le principe ainsi que la réalisation d'une technique de réduction du bruit originale s'inspirant du filtrage de Wiener, dans le but de s'affranchir du bruit environnemental transmis aux systèmes considérés. Dans les deux derniers chapitres, nous étudions expérimentalement et théoriquement les fluctuations du travail ainsi que de la production de chaleur de petits oscillateurs mécaniques dissipatifs portés dans des états hors d'équilibre.This thesis presents an experimental study of work and heat fluctuations of mechanical systems driven out of equilibrium. The aim is to test recent theoretical approaches mainly due to Jarzynski, Crooks, Gallavotti, Cohen, van Zon and coworkers. In a first chapter, we introduce these new results and motivate the need for performing experiments to test them. The second chapter is dedicated to the principles and to the experimental apparatus and device: a differential interferometer, inspired from the Nomarski technique, allows us to measure the thermal sub-nanometric displacements of mechanical dissipative oscillators. A third chapter is dedicated to the principle and to the setup of a new denoising technique inspired from Wiener's filtering. This technique allows us to strongly reduce the environmental noise transmitted to the experimental systems of interest. In the last two chapters, we experimentally and theoretically study work and heat production thermal fluctuations of small mechanical dissipative oscillators driven out of equilibrium.LYON-ENS Sciences (693872304) / SudocSudocFranceF

MUSCL scheme for Single Well Chemical Tracer Test simulation, design and interpretation

Our paper presents an improved numerical scheme to simulate Single Well Chemical Tracer Test (SWCTT) method. SWCTT is mainly applied to determine the residual oil saturation of reservoirs. It consists in injecting an aqueous slug of a primary tracer into the reservoir formation and displacing it at a certain distance from the well. This tracer is partly miscible with oil on the one hand, and generates in situ a secondary tracer on the other hand. As a consequence, a shift is observed between the primary and the secondary tracers arrival times when production is resumed. This time shift is used to evaluate the residual oil saturation. In our paper, we propose a numerical scheme based on a fractional time stepping technique to decouple the resolution of the phases mass conservation equations and the chemical tracers mole conservation equations. For the phases resolution, we use an implicit scheme to ensure stability and robustness. For the chemical tracers, we propose an explicit second-order scheme in time and in space via MUSCL technique to improve the tracers time-shift calculation. The proposed numerical method is implemented on a realistic simulation model consisting of a vertical well crossing a reservoir consisting of a stack of homogeneous layers. By reducing the numerical dispersion, the proposed scheme improves the accuracy of predicted concentration profiles, without significantly increasing the computation time. Finally, the advantages of using a second-order scheme for residual oil saturation assessment are discussed on the basis of a radial 1D mesh convergence study

MUSCL scheme for Single Well Chemical Tracer Test simulation, design and interpretation

Our paper presents an improved numerical scheme to simulate Single Well Chemical Tracer Test (SWCTT) method. SWCTT is mainly applied to determine the residual oil saturation of reservoirs. It consists in injecting an aqueous slug of a primary tracer into the reservoir formation and displacing it at a certain distance from the well. This tracer is partly miscible with oil on the one hand, and generates in situ a secondary tracer on the other hand. As a consequence, a shift is observed between the primary and the secondary tracers arrival times when production is resumed. This time shift is used to evaluate the residual oil saturation. In our paper, we propose a numerical scheme based on a fractional time stepping technique to decouple the resolution of the phases mass conservation equations and the chemical tracers mole conservation equations. For the phases resolution, we use an implicit scheme to ensure stability and robustness. For the chemical tracers, we propose an explicit second-order scheme in time and in space via MUSCL technique to improve the tracers time-shift calculation. The proposed numerical method is implemented on a realistic simulation model consisting of a vertical well crossing a reservoir consisting of a stack of homogeneous layers. By reducing the numerical dispersion, the proposed scheme improves the accuracy of predicted concentration profiles, without significantly increasing the computation time. Finally, the advantages of using a second-order scheme for residual oil saturation assessment are discussed on the basis of a radial 1D mesh convergence study