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

Microscopic heat from the energetics of stochastic phenomena

The energetics of the stochastic process has shown the balance of energy on the mesoscopic level. The heat and the energy defined there are, however, generally different from their macroscopic counterpart. We show that this discrepancy can be removed by adding to these quantities the reversible heat associated with the mesoscopic free energy.Comment: 4 pages, 0 figur

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

Nonlinear internal wave penetration via parametric subharmonic instability

6 pages, 5 figuresInternational audienceWe present the results of a laboratory experimental study of an internal wave field generated by harmonic, spatially-periodic boundary forcing from above of a density stratification comprising a strongly-stratified, thin upper layer sitting atop a weakly-stratified, deep lower layer. In linear regimes, the energy flux associated with relatively high frequency internal waves excited in the upper layer is prevented from entering the lower layer by virtue of evanescent decay of the wave field. In the experiments, however, we find that the development of parametric subharmonic instability (PSI) in the upper layer transfers energy from the forced primary wave into a pair of subharmonic daughter waves, each capable of penetrating the weakly-stratified lower layer. We find that around $10\%$ of the primary wave energy flux penetrates into the lower layer via this nonlinear wave-wave interaction for the regime we study

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

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

Nonlinear internal wave penetration via parametric subharmonic instability

We present the results of a laboratory experimental study of an internal wave field generated by harmonic, spatially periodic boundary forcing from above of a density stratification comprising a strongly stratified, thin upper layer sitting atop a weakly stratified, deep lower layer. In linear regimes, the energy flux associated with relatively high frequency internal waves excited in the upper layer is prevented from entering the lower layer by virtue of evanescent decay of the wave field. In the experiments, however, we find that the development of parametric subharmonic instability in the upper layer transfers energy from the forced primary wave into a pair of subharmonic daughter waves, each capable of penetrating the weakly stratified lower layer. We find that around 10% of the primary wave energy flux penetrates into the lower layer via this nonlinear wave-wave interaction for the regime we study.ONLITUR ((No. ANR-2011-BS04-006-01)National Science Foundation (U.S.) (No. OCE-1357434

Entropy production and fluctuation theorems under feedback control: the molecular refrigerator model revisited

We revisit the model of a Brownian particle in a heat bath submitted to an actively controlled force proportional to the velocity that leads to thermal noise reduction (cold damping). We investigate the influence of the continuous feedback on the fluctuations of the total entropy production and show that the explicit expression of the detailed fluctuation theorem involves different dynamics and observables in the forward and backward processes. As an illustration, we study the analytically solvable case of a harmonic oscillator and calculate the characteristic function of the entropy production in a nonequilibrium steady state. We then determine the corresponding large deviation function which results from an unusual interplay between 'boundary' and 'bulk' contributions.Comment: 16 pages, 5 figures. References 9,10,13,14,15 added. A few changes in the text. Accepted for publication in J. Stat. Mec

Exponential peak and scaling of work fluctuations in modulated systems

We extend the stationary-state work fluctuation theorem to periodically modulated nonlinear systems. Such systems often have coexisting stable periodic states. We show that work fluctuations sharply increase near a kinetic phase transition where the state populations are close to each other. The work variance is proportional here to the reciprocal rate of interstate switching. We also show that the variance displays scaling with the distance to a bifurcation point and find the critical exponent for a saddle-node bifurcation