Work fluctuation theorems for harmonic oscillators

The work fluctuations of an oscillator in contact with a thermostat and driven out of equilibrium by an external force are studied experimentally and theoretically within the context of Fluctuation Theorems (FTs). The oscillator dynamics is modeled by a second order Langevin equation. Both the transient and stationary state fluctuation theorems hold and the finite time corrections are very different from those of a first order Langevin equation. The periodic forcing of the oscillator is also studied; it presents new and unexpected short time convergences. Analytical expressions are given in all cases

Fluctuation theorems for harmonic oscillators

We study experimentally the thermal fluctuations of energy input and dissipation in a harmonic oscillator driven out of equilibrium, and search for Fluctuation Relations. We study transient evolution from the equilibrium state, together with non equilibrium steady states. Fluctuations Relations are obtained experimentally for both the work and the heat, for the stationary and transient evolutions. A Stationary State Fluctuation Theorem is verified for the two time prescriptions of the torque. But a Transient Fluctuation Theorem is satisfied for the work given to the system but not for the heat dissipated by the system in the case of linear forcing. Experimental observations on the statistical and dynamical properties of the fluctuation of the angle, we derive analytical expressions for the probability density function of the work and the heat. We obtain for the first time an analytic expression of the probability density function of the heat. Agreement between experiments and our modeling is excellent

Steady state fluctuation relations for systems driven by an external random force

We experimentally study the fluctuations of the work done by an external Gaussian random force on two different stochastic systems coupled to a thermal bath: a colloidal particle in an optical trap and an atomic force microscopy cantilever. We determine the corresponding probability density functions for different random forcing amplitudes ranging from a small fraction to several times the amplitude of the thermal noise. In both systems for sufficiently weak forcing amplitudes the work fluctuations satisfy the usual steady state fluctuation theorem. As the forcing amplitude drives the system far from equilibrium, deviations of the fluctuation theorem increase monotonically. The deviations can be recasted to a single master curve which only depends on the kind of stochastic external force.Comment: 6 pages, submitted to EP

Thermodynamic time asymmetry in nonequilibrium fluctuations

We here present the complete analysis of experiments on driven Brownian motion and electric noise in a $RC$ circuit, showing that thermodynamic entropy production can be related to the breaking of time-reversal symmetry in the statistical description of these nonequilibrium systems. The symmetry breaking can be expressed in terms of dynamical entropies per unit time, one for the forward process and the other for the time-reversed process. These entropies per unit time characterize dynamical randomness, i.e., temporal disorder, in time series of the nonequilibrium fluctuations. Their difference gives the well-known thermodynamic entropy production, which thus finds its origin in the time asymmetry of dynamical randomness, alias temporal disorder, in systems driven out of equilibrium.Comment: to be published in : Journal of Statistical Mechanics: theory and experimen

Experimental study of out of equilibrium fluctuations in a colloidal suspension of Laponite using optical traps

This work is devoted to the study of displacement fluctuations of micron-sized particles in an aging colloidal glass. We address the issue of the validity of the fluctuation dissipation theorem (FDT) and the time evolution of viscoelastic properties during aging of aqueous suspensions of a clay (Laponite RG) in a colloidal glass phase. Given the conflicting results reported in the literature for different experimental techniques, our goal is to check and reconcile them using \emph{simultaneously} passive and active microrheology techniques. For this purpose we measure the thermal fluctuations of micro-sized brownian particles immersed in the colloidal glass and trapped by optical tweezers. We find that both microrheology techniques lead to compatible results even at low frequencies and no violation of FDT is observed. Several interesting features concerning the statistical properties and the long time correlations of the particles are observed during the transition

Fluctuation theorems for stochastic dynamics

Fluctuation theorems make use of time reversal to make predictions about entropy production in many-body systems far from thermal equilibrium. Here we review the wide variety of distinct, but interconnected, relations that have been derived and investigated theoretically and experimentally. Significantly, we demonstrate, in the context of Markovian stochastic dynamics, how these different fluctuation theorems arise from a simple fundamental time-reversal symmetry of a certain class of observables. Appealing to the notion of Gibbs entropy allows for a microscopic definition of entropy production in terms of these observables. We work with the master equation approach, which leads to a mathematically straightforward proof and provides direct insight into the probabilistic meaning of the quantities involved. Finally, we point to some experiments that elucidate the practical significance of fluctuation relations.Comment: 48 pages, 2 figures. v2: minor changes for consistency with published versio

Fluctuations of the total entropy production in stochastic systems

Fluctuations of the excess heat in an out of equilibrium steady state are experimentally investigated in two stochastic systems : an electric circuit with an imposed mean current and a harmonic oscillator driven out of equilibrium by a periodic torque. In these two linear systems, we study excess heat that represents the difference between the dissipated heat out of equilibrium and the dissipated heat at equilibrium. Fluctuation theorem holds for the excess heat in the two experimental systems for all observation times and for all fluctuation magnitudes.Comment: 6

Fluctuation Relations for Diffusion Processes

The paper presents a unified approach to different fluctuation relations for classical nonequilibrium dynamics described by diffusion processes. Such relations compare the statistics of fluctuations of the entropy production or work in the original process to the similar statistics in the time-reversed process. The origin of a variety of fluctuation relations is traced to the use of different time reversals. It is also shown how the application of the presented approach to the tangent process describing the joint evolution of infinitesimally close trajectories of the original process leads to a multiplicative extension of the fluctuation relations.Comment: 38 page

Wringing out DNA

The chiral nature of DNA plays a crucial role in cellular processes. Here we use magnetic tweezers to explore one of the signatures of this chirality, the coupling between stretch and twist deformations. We show that the extension of a stretched DNA molecule increases linearly by 0.42 nm per excess turn applied to the double helix. This result contradicts the intuition that DNA should lengthen as it is unwound and get shorter with overwinding. We then present numerical results of energy minimizations of torsionally restrained DNA that display a behaviour similar to the experimental data and shed light on the molecular details of this surprising effect.Comment: 4 pages revtex4, 4 figure

Reproducibility of blood tests of liver fibrosis in clinical practice

Objectives:To evaluate the inter-laboratory reproducibility of blood test for liver fibrosis: FibroMeter, Fibrotest, APRI and their composites variables. Design and methods: Four studies, including 147 patients, were performed: study #1 included 2 metachronous blood samples and 2 laboratories; studies #2, #3 and #4 included synchronous samples with assays delayed at day 1 in 12 laboratories, at day 0 in 10 laboratories and at day 0 or 1 in 2 laboratories, respectively. Agreement was evaluated by the intraclass correlation coefficient (ric). Results: In studies #1, #2 and #4, ric for FibroMeter was 0.893, 0.942 and 0.991, respectively. In study #3, the ric were: FibroMeter: 0.963, Fibrotest: 0.984, APRI: 0.949. Large simulated variations in composite variables had a weak impact on FibroMeter. Conclusions: When blood marker limits are controlled, inter-laboratory agreement of blood tests is excellent in clinical practice conditions. Blood tests are robust against the variability of composite blood variables