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.PACS numbers: 84.30.Bv, In this letter, we investigate, within the context of the Fluctuation Theorems (FTs), the work fluctuations of a harmonic oscillator in contact with a thermostat and driven out of equilibrium by an external force. First found in dynamical systems [1,2] and later extended to stochastic systems [3,4,5,6], these conventional FTs give a relation between the probabilities to observe a positive value of the (time averaged) "entropy production rate" and a negative one. This relation is of the form P (σ)/P (−σ) = exp [στ ], where σ and −σ are equal but opposite values for the entropy production rate, P (σ) and P (−σ) give their probabilities and τ is the length of the interval over which σ is measured. In these systems, the above mentioned FT is derived for a mathematical quantity σ, which has a form similar to that of the entropy production rate in Irreversible Thermodynamics [7].The proof of FTs is based on a certain number of hypothesis; experimenting on a real device is useful not only to check those hypothesis, but also to observe whether the predicted effects are observable or remain only a theoretical tool. There are not many experimental tests of FTs. Some of them are performed in dynamical systems [8] in which the interpretation of the results is very difficult. Other experiments are performed on stochastic systems, one on a Brownian particle in a moving optical trap [9] and another on electrical circuits driven out of equilibrium by injecting in it a small current [10]. The last two systems are described by first order Langevin equations and the results agree with the predictions of ref. [5,6]. As far as we know no theoretical predictions are available for systems described by a second order Langevin equation. The test using an harmonic oscillator is particularly important because the harmonic oscillator is the basis of many physical processes. Indeed the general predictions of FTs are valid only for τ → ∞ and the corrections for finite τ have been computed only for a first order Langevin dynamics.In the present letter, we address several important questions. We investigate first the Transient Fluctuation Theorem (TFT) of the total external work done on the system in the transient state, i.e., considering a time interval of duration τ which starts immediately after the external force has been applied to the oscillator. We then analyze the Stationary State Fluctuation Theorem (SSFT) which c...

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 behavior similar to the experimental data and shed light on the molecular details of this surprising effect.

Internal waves are believed to be of primary importance as they affect ocean mixing and energy transport. Several processes can lead to the breaking of internal waves and they usually involve non linear interactions between waves. In this work, we study experimentally the parametric subharmonic instability (PSI), which provides an efficient mechanism to transfer energy from large to smaller scales. It corresponds to the destabilization of a primary plane wave and the spontaneous emission of two secondary waves, of lower frequencies and different wave vectors. Using a time-frequency analysis, we observe the time evolution of the secondary waves, thus measuring the growth rate of the instability. In addition, a Hilbert transform method allows the measurement of the different wave vectors. We compare these measurements with theoretical predictions, and study the dependence of the instability with primary wave frequency and amplitude, revealing a possible effect of the confinement due to the finite size of the beam, on the selection of the unstable mode.

The time-reversal symmetry of nonequilibrium fluctuations is experimentally investigated in two out-of-equilibrium systems: namely, a Brownian particle in a trap moving at constant speed and an electric circuit with an imposed mean current. The dynamical randomness of their nonequilibrium fluctuations is characterized in terms of the standard and time-reversed entropies per unit time of dynamical systems theory. We present experimental results showing that their difference equals the thermodynamic entropy production in units of Boltzmann's constant.

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.

Abstract. 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.

-One of the pivotal questions in the dynamics of the oceans is related to the cascade of mechanical energy in the abyss and its contribution to mixing. Here, we propose internal wave attractors in the large amplitude regime as a unique self-consistent experimental and numerical setup that models a cascade of triadic interactions transferring energy from large-scale monochromatic input to multi-scale internal wave motion. We also provide signatures of a discrete wave turbulence framework for internal waves. Finally, we show how beyond this regime, we have a clear transition to a regime of small-scale high-vorticity events which induce mixing.Introduction. -The continuous energy input to the ocean interior comes from the interaction of global tides with the bottom topography [1]. The subsequent mechanical energy cascade to small-scale internal-wave motion and mixing is a subject of active debate [2] in view of the important role played by abyssal mixing in existing models of ocean dynamics [3][4][5]. A question remains: how does energy injected through internal waves at large vertical scales [6] induce the mixing of the fluid [2]?In a stratified fluid with an initially constant buoyancy frequency N = [(−g/ρ)(dρ/dz)] 1/2 , where ρ(z) is the density distribution (ρ a reference value) over vertical coordinate z, and g the gravity acceleration, the dispersion relation of internal waves is θ = ± arcsin(Ω). The angle θ is the slope of the wave beam to the horizontal, and Ω the frequency of oscillations non-dimensionalized by N . The dispersion relation requires preservation of the slope of the internal wave beam upon reflection at a rigid boundary. In the case of a sloping boundary, this property gives a purely geometric reason for a strong variation of the width of internal wave beams (focusing or defocusing) upon reflection. Internal wave focusing provides a necessary condition for large shear and overturning, as well as shear and bottom layer instabilities at slopes [7][8][9][10].In a confined fluid domain, focusing usually prevails, leading to a concentration of wave energy on a closed loop, the internal wave attractor [11]. Attractors eventually

Internal gravity waves play a primary role in geophysical fluids: they contribute significantly to mixing in the ocean and they redistribute energy and momentum in the middle atmosphere. Until recently, most studies were focused on plane wave solutions. However, these solutions are not a satisfactory description of most geophysical manifestations of internal gravity waves, and it is now recognized that internal wave beams with a confined profile are ubiquitous in the geophysical context. We will discuss the reason for the ubiquity of wave beams in stratified fluids, related to the fact that they are solutions of the nonlinear governing equations. We will focus more specifically on situations with a constant buoyancy frequency. Moreover, in light of recent experimental and analytical studies of internal gravity beams, it is timely to discuss the two main mechanisms of instability for those beams. i) The Triadic Resonant Instability generating two secondary wave beams. ii) The streaming instability corresponding to the spontaneous generation of a mean flow.