Experimental study of work fluctuations in a harmonic oscillator

The work fluctuations of a harmonic oscillator in contact with a thermostat and driven out of equilibrium by an external force are studied experimentally. For the work both the transient and stationary state fluctuation theorems hold. The finite time corrections are very different from those of a first order Langevin equation. The heat and work fluctuations are studied when a periodic forcing is applied to the oscillator. The importance of the choice of the ''good work'' to compute the free energy from the Jarzinsky equality is discussed

A simple proof of the Jarzynski equality?

In this short communication, I give a very simple derivation of the Jarzynski equality, which allows to compute the free energy difference of a body, which is driven between two equilibrium states $A$ and $B$ by an external (time-dependent) force, from the probability distribution function of the work done on the system, regardless of the nature of the transformation (reversible or irreversible) between the states $A$ and $B$. It perhaps throws some light on the debate recently started by Cohen and coworkers , and perhaps explains why all the experiments which has been performed in order to test the Jarzynski equality are successful, even in very defavorable (irreversible) cases (and more strikingly, when the state $B$ is not an equilibrium one)

Turning bacteria suspensions into a "superfluid"

The rheological response under simple shear of an active suspension of Escherichia coli is determined in a large range of shear rates and concentrations. The effective viscosity and the time scales characterizing the bacterial organization under shear are obtained. In the dilute regime, we bring evidences for a low shear Newtonian plateau characterized by a shear viscosity decreasing with concentration. In the semi-dilute regime, for particularly active bacteria, the suspension display a "super-fluid" like transition where the viscous resistance to shear vanishes, thus showing that macroscopically, the activity of pusher swimmers organized by shear, is able to fully overcome the dissipative effects due to viscous loss

Experimental Test of a New Equality: Measuring Heat Dissipation in an Optically Driven Colloidal System

Measurement of energy dissipation in small nonequilibrium systems is generally a difficult task. Recently, Harada and Sasa [Phys.Rev.Lett. 95, 130602(2005)] derived an equality relating the energy dissipation rate to experimentally accessible quantities in nonequilibrium steady states described by the Langevin equation. Here, we show the first experimental test of this new relation in an optically driven colloidal system. We find that this equality is validated to a fairly good extent, thus the irreversible work of a small system is estimated from readily obtainable quantities.Comment: 4 pages, 6 figure

Single beam interferometric angle measurement

We present an application of a quadrature phase interferometer to the measurement of the angular position of a parallel laser beam with interferometric precision. In our experimental realization we reach a resolution of 6.8e-10 rad (1.4e-4 arcsec) for 1 kHz bandwidth in a 2e-2 rad (1 deg) range. This alternative to the optical lever technique features absolute calibration, independence of the sensitivity on the thermal drifts, and wide range of measurement at full accuracy

Protein-Mediated DNA Loops: Effects of Protein Bridge Size and Kinks

This paper focuses on the probability that a portion of DNA closes on itself through thermal fluctuations. We investigate the dependence of this probability upon the size r of a protein bridge and/or the presence of a kink at half DNA length. The DNA is modeled by the Worm-Like Chain model, and the probability of loop formation is calculated in two ways: exact numerical evaluation of the constrained path integral and the extension of the Shimada and Yamakawa saddle point approximation. For example, we find that the looping free energy of a 100 base pairs DNA decreases from 24 kT to 13 kT when the loop is closed by a protein of r = 10 nm length. It further decreases to 5 kT when the loop has a kink of 120 degrees at half-length.Comment: corrected typos and figures, references updated; 13 pages, 7 figures, accepted for publication in Phys. Rev.

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

An experimental test of the Jarzynski equality in a mechanical experiment

We have experimentally checked the Jarzynski equality and the Crooks relation on the thermal fluctuations of a macroscopic mechanical oscillator in contact with a heat reservoir. We found that, independently of the time scale and amplitude of the driving force, both relations are satisfied. These results give credit, at least in the case of Gaussian fluctuations, to the use of these relations in biological and chemical systems to estimate the free energy difference between two equilibrium states. An alternative method to estimate of the free nergy difference in isothermal process is proposed too.Comment: submitted to Europhysics Letter