Fluctuations in out of equilibrium systems: from theory to experiment

Abstract

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 details. Finally we will discuss the problems related to the applications of fluctuation theorems to chaotic systems.

Submitted to JSTAT

References in corpus (19)

• An Extension of the Fluctuation Theorem
• Nonequilibrium fluctuations in a resistor
• Stationary and Transient Work-Fluctuation Theorems for a Dragged Brownian Particle
• Extended Heat-Fluctuation Theorems for a System with Deterministic and Stochastic Forces
• Power and heat fluctuation theorems for electric circuits
• Work fluctuation theorems for harmonic oscillators
• A fluidized granular medium as an instance of the Fluctuation Theorem
• Fluctuation theorems for harmonic oscillators
• Fluctuations of internal energy flow in a vibrated granular gas
• The Steady State Fluctuation Relation for the Dissipation Function
• Work and dissipation fluctuations near the stochastic resonance of a colloidal particle
• Relevance of initial and final conditions for the Fluctuation Relation in Markov processes
• Granular Brownian motion
• A Granular Brownian Ratchet Model
• Probability density functions of work and heat near the stochastic resonance of a colloidal particle
• Granular Brownian Motor
• Fluctuations of the total entropy production in stochastic systems
• Statistics of power injection in a plate set into chaotic vibration
• Is it possible to experimentally verify the fluctuation relation? A review of theoretical motivations and numerical evidence

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