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.