108 research outputs found
Fluctuations relations for semiclassical single-mode laser
Over last decades, the study of laser fluctuations has shown that laser
theory may be regarded as a prototypical example of a nonlinear nonequilibrium
problem. The present paper discusses the fluctuation relations, recently
derived in nonequilibrium statistical mechanics, in the context of the
semiclassical laser theory.Comment: 11 pages, 3 figure
Fluctuation-Dissipation Theorem in Nonequilibrium Steady States
In equilibrium, the fluctuation-dissipation theorem (FDT) expresses the
response of an observable to a small perturbation by a correlation function of
this variable with another one that is conjugate to the perturbation with
respect to \emph{energy}. For a nonequilibrium steady state (NESS), the
corresponding FDT is shown to involve in the correlation function a variable
that is conjugate with respect to \emph{entropy}. By splitting up entropy
production into one of the system and one of the medium, it is shown that for
systems with a genuine equilibrium state the FDT of the NESS differs from its
equilibrium form by an additive term involving \emph{total} entropy production.
A related variant of the FDT not requiring explicit knowledge of the stationary
state is particularly useful for coupled Langevin systems. The \emph{a priori}
surprising freedom apparently involved in different forms of the FDT in a NESS
is clarified.Comment: 6 pages; EPL, in pres
Level 2.5 large deviations for continuous time Markov chains with time periodic rates
We consider an irreducible continuous time Markov chain on a finite state
space and with time periodic jump rates and prove the joint large deviation
principle for the empirical measure and flow and the joint large deviation
principle for the empirical measure and current. By contraction we get the
large deviation principle of three types of entropy production flow. We derive
some Gallavotti-Cohen duality relations and discuss some applications.Comment: 37 pages. corrected versio
Modified Fluctuation-dissipation theorem for non-equilibrium steady-states and applications to molecular motors
We present a theoretical framework to understand a modified
fluctuation-dissipation theorem valid for systems close to non-equilibrium
steady-states and obeying markovian dynamics. We discuss the interpretation of
this result in terms of trajectory entropy excess. The framework is illustrated
on a simple pedagogical example of a molecular motor. We also derive in this
context generalized Green-Kubo relations similar to the ones derived recently
by Seifert., Phys. Rev. Lett., 104, 138101 (2010) for more general networks of
biomolecular states.Comment: 6 pages, 2 figures, submitted in EP
Finite sampling effects on generalized fluctuation-dissipation relations for steady states
We study the effects of the finite number of experimental data on the
computation of a generalized fluctuation-dissipation relation around a
nonequilibrium steady state of a Brownian particle in a toroidal optical trap.
We show that the finite sampling has two different effects, which can give rise
to a poor estimate of the linear response function. The first concerns the
accessibility of the generalized fluctuation-dissipation relation due to the
finite number of actual perturbations imposed to the control parameter. The
second concerns the propagation of the error made at the initial sampling of
the external perturbation of the system. This can be highly enhanced by
introducing an estimator which corrects the error of the initial sampled
condition. When these two effects are taken into account in the data analysis,
the generalized fluctuation-dissipation relation is verified experimentally
Fluctuations and response in a non-equilibrium micron-sized system
The linear response of non-equilibrium systems with Markovian dynamics
satisfies a generalized fluctuation-dissipation relation derived from time
symmetry and antisymmetry properties of the fluctuations. The relation involves
the sum of two correlation functions of the observable of interest: one with
the entropy excess and the second with the excess of dynamical activity with
respect to the unperturbed process, without recourse to anything but the
dynamics of the system. We illustrate this approach in the experimental
determination of the linear response of the potential energy of a Brownian
particle in a toroidal optical trap. The overdamped particle motion is
effectively confined to a circle, undergoing a periodic potential and driven
out of equilibrium by a non-conservative force. Independent direct and indirect
measurements of the linear response around a non-equilibrium steady state are
performed in this simple experimental system. The same ideas are applicable to
the measurement of the response of more general non-equilibrium micron-sized
systems immersed in Newtonian fluids either in stationary or non-stationary
states and possibly including inertial degrees of freedom.Comment: 12 pages, submitted to J. Stat. Mech., revised versio
Probing active forces via a fluctuation-dissipation relation: Application to living cells
We derive a new fluctuation-dissipation relation for non-equilibrium systems
with long-term memory. We show how this relation allows one to access new
experimental information regarding active forces in living cells that cannot
otherwise be accessed. For a silica bead attached to the wall of a living cell,
we identify a crossover time between thermally controlled fluctuations and
those produced by the active forces. We show that the probe position is
eventually slaved to the underlying random drive produced by the so-called
active forces.Comment: 5 page
Entropy production and fluctuation relations for a KPZ interface
We study entropy production and fluctuation relations in the restricted
solid-on-solid growth model, which is a microscopic realization of the KPZ
equation. Solving the one dimensional model exactly on a particular line of the
phase diagram we demonstrate that entropy production quantifies the distance
from equilibrium. Moreover, as an example of a physically relevant current
different from the entropy, we study the symmetry of the large deviation
function associated with the interface height. In a special case of a system of
length L=4 we find that the probability distribution of the variation of height
has a symmetric large deviation function, displaying a symmetry different from
the Gallavotti-Cohen symmetry.Comment: 21 pages, 5 figure
Linear response theory and transient fluctuation theorems for diffusion processes: a backward point of view
On the basis of perturbed Kolmogorov backward equations and path integral
representation, we unify the derivations of the linear response theory and
transient fluctuation theorems for continuous diffusion processes from a
backward point of view. We find that a variety of transient fluctuation
theorems could be interpreted as a consequence of a generalized
Chapman-Kolmogorov equation, which intrinsically arises from the Markovian
characteristic of diffusion processes
The fluctuation-dissipation relation: how does one compare correlation functions and responses?
We discuss the well known Einstein and the Kubo Fluctuation Dissipation
Relations (FDRs) in the wider framework of a generalized FDR for systems with a
stationary probability distribution. A multi-variate linear Langevin model,
which includes dynamics with memory, is used as a treatable example to show how
the usual relations are recovered only in particular cases. This study brings
to the fore the ambiguities of a check of the FDR done without knowing the
significant degrees of freedom and their coupling. An analogous scenario
emerges in the dynamics of diluted shaken granular media. There, the
correlation between position and velocity of particles, due to spatial
inhomogeneities, induces violation of usual FDRs. The search for the
appropriate correlation function which could restore the FDR, can be more
insightful than a definition of ``non-equilibrium'' or ``effective
temperatures''.Comment: 22 pages, 9 figure
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