66 research outputs found
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
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
Work fluctuations in a nematic liquid crystal
The orientation fluctuations of the director of a liquid crystal are
measured, by a sensitive polarization interferometer, close to the
Fr\'eedericksz transition, which is a second order transition driven by an
electric field. Using mean field theory, we define the work injected into the
system by a change of the electric field and we calibrate it using
Fluctuation-Dissipation Theorem. We show that the work fluctuations satisfy the
Transient Fluctuation Theorem. An analytical justification of this result is
given. The open problems for the out of equilibrium case are finally discussed.Comment: to be published in JSTAT: theory and experiment
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 of the primary wave energy flux penetrates into the lower layer via this nonlinear wave-wave interaction for the regime we study
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
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
Aging and effective temperatures near a critical point
The orientation fluctuations of the director of a liquid crystal(LC) are
measured after a quench near the Fr\'eedericksz transition, which is a second
order transition driven by an electric field. We report experimental evidence
that, because of the critical slowing down, the LC presents, after the quench,
several properties of an aging system, such as power law scaling versus time of
correlation and response functions. During this slow relaxation, a well defined
effective temperature, much larger than the heat bath temperature, can be
measured using the fluctuation dissipation relation.Comment: to be published in PR
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