44 research outputs found
Langevin dynamics with space-time periodic nonequilibrium forcing
We present results on the ballistic and diffusive behavior of the Langevin
dynamics in a periodic potential that is driven away from equilibrium by a
space-time periodic driving force, extending some of the results obtained by
Collet and Martinez. In the hyperbolic scaling, a nontrivial average velocity
can be observed even if the external forcing vanishes in average. More
surprisingly, an average velocity in the direction opposite to the forcing may
develop at the linear response level -- a phenomenon called negative mobility.
The diffusive limit of the non-equilibrium Langevin dynamics is also studied
using the general methodology of central limit theorems for additive
functionals of Markov processes. To apply this methodology, which is based on
the study of appropriate Poisson equations, we extend recent results on
pointwise estimates of the resolvent of the generator associated with the
Langevin dynamics. Our theoretical results are illustrated by numerical
simulations of a two-dimensional system
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
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
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
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
Thermodynamic time asymmetry in nonequilibrium fluctuations
We here present the complete analysis of experiments on driven Brownian
motion and electric noise in a 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
Correcting the extended-source calibration for the <i>Herschel</i>-SPIRE Fourier-transform spectrometer
We describe an update to the Herschel-Spectral and Photometric Imaging Receiver (SPIRE) Fourier-transform spectrometer (FTS) calibration for extended sources, which incorporates a correction for the frequency-dependent far-field feedhorn efficiency, ηff. This significant correction affects all FTS extended-source calibrated spectra in sparse or mapping mode, regardless of the spectral resolution. Line fluxes and continuum levels are underestimated by factors of 1.3–2 in thespectrometer long wavelength band (447–1018 GHz; 671–294 μm) and 1.4–1.5 in the spectrometer short wavelength band (944–1568 GHz; 318–191 μm). The correction was implemented in the FTS pipeline version 14.1 and has also been described in the SPIRE Handbook since 2017 February. Studies based on extended-source calibrated spectra produced prior to this pipeline version should be critically reconsidered using the current products available in the Herschel Science Archive. Once the extended-source calibrated spectra are corrected for ηff, the synthetic photometry and the broad-band intensities from SPIRE photometer maps agree within 2–4 per cent – similar levels to the comparison of point-source calibrated spectra and photometry from point-source calibrated maps. The two calibration schemes for the FTS are now self-consistent: the conversion between the corrected extended-source and point-source calibrated spectra can be achieved with the beam solid angle and a gain correction that accounts for the diffraction loss
Fluctuation theorems for stochastic dynamics
Fluctuation theorems make use of time reversal to make predictions about
entropy production in many-body systems far from thermal equilibrium. Here we
review the wide variety of distinct, but interconnected, relations that have
been derived and investigated theoretically and experimentally. Significantly,
we demonstrate, in the context of Markovian stochastic dynamics, how these
different fluctuation theorems arise from a simple fundamental time-reversal
symmetry of a certain class of observables. Appealing to the notion of Gibbs
entropy allows for a microscopic definition of entropy production in terms of
these observables. We work with the master equation approach, which leads to a
mathematically straightforward proof and provides direct insight into the
probabilistic meaning of the quantities involved. Finally, we point to some
experiments that elucidate the practical significance of fluctuation relations.Comment: 48 pages, 2 figures. v2: minor changes for consistency with published
versio