68 research outputs found
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
Fluctuation Relations for Diffusion Processes
The paper presents a unified approach to different fluctuation relations for
classical nonequilibrium dynamics described by diffusion processes. Such
relations compare the statistics of fluctuations of the entropy production or
work in the original process to the similar statistics in the time-reversed
process. The origin of a variety of fluctuation relations is traced to the use
of different time reversals. It is also shown how the application of the
presented approach to the tangent process describing the joint evolution of
infinitesimally close trajectories of the original process leads to a
multiplicative extension of the fluctuation relations.Comment: 38 page
Quantum Fluctuation Relations for the Lindblad Master Equation
An open quantum system interacting with its environment can be modeled under
suitable assumptions as a Markov process, described by a Lindblad master
equation. In this work, we derive a general set of fluctuation relations for
systems governed by a Lindblad equation. These identities provide quantum
versions of Jarzynski-Hatano-Sasa and Crooks relations. In the linear response
regime, these fluctuation relations yield a fluctuation-dissipation theorem
(FDT) valid for a stationary state arbitrarily far from equilibrium. For a
closed system, this FDT reduces to the celebrated Callen-Welton-Kubo formula
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
Time-ordering and a generalized Magnus expansion
Both the classical time-ordering and the Magnus expansion are well-known in
the context of linear initial value problems. Motivated by the noncommutativity
between time-ordering and time derivation, and related problems raised recently
in statistical physics, we introduce a generalization of the Magnus expansion.
Whereas the classical expansion computes the logarithm of the evolution
operator of a linear differential equation, our generalization addresses the
same problem, including however directly a non-trivial initial condition. As a
by-product we recover a variant of the time ordering operation, known as
T*-ordering. Eventually, placing our results in the general context of
Rota-Baxter algebras permits us to present them in a more natural algebraic
setting. It encompasses, for example, the case where one considers linear
difference equations instead of linear differential equations
Two refreshing views of Fluctuation Theorems through Kinematics Elements and Exponential Martingale
In the context of Markov evolution, we present two original approaches to
obtain Generalized Fluctuation-Dissipation Theorems (GFDT), by using the
language of stochastic derivatives and by using a family of exponential
martingales functionals. We show that GFDT are perturbative versions of
relations verified by these exponential martingales. Along the way, we prove
GFDT and Fluctuation Relations (FR) for general Markov processes, beyond the
usual proof for diffusion and pure jump processes. Finally, we relate the FR to
a family of backward and forward exponential martingales.Comment: 41 pages, 7 figures; version2: 45 pages, 7 figures, minor revisions,
new results in Section
Mechanical Responses and Stress Fluctuations of a Supercooled Liquid in a Sheared Non-Equilibrium State
A steady shear flow can drive supercooled liquids into a non-equilibrium
state. Using molecular dynamics simulations under steady shear flow
superimposed with oscillatory shear strain for a probe, non-equilibrium
mechanical responses are studied for a model supercooled liquid composed of
binary soft spheres. We found that even in the strongly sheared situation, the
supercooled liquid exhibits surprisingly isotropic responses to oscillating
shear strains applied in three different components of the strain tensor. Based
on this isotropic feature, we successfully constructed a simple two-mode
Maxwell model that can capture the key features of the storage and loss moduli,
even for highly non-equilibrium state. Furthermore, we examined the correlation
functions of the shear stress fluctuations, which also exhibit isotropic
relaxation behaviors in the sheared non-equilibrium situation. In contrast to
the isotropic features, the supercooled liquid additionally demonstrates
anisotropies in both its responses and its correlations to the shear stress
fluctuations. Using the constitutive equation (a two-mode Maxwell model), we
demonstrated that the anisotropic responses are caused by the coupling between
the oscillating strain and the driving shear flow. We measured the magnitude of
this violation in terms of the effective temperature. It was demonstrated that
the effective temperature is notably different between different components,
which indicates that a simple scalar mapping, such as the concept of an
effective temperature, oversimplifies the true nature of supercooled liquids
under shear flow. An understanding of the mechanism of isotropies and
anisotropies in the responses and fluctuations will lead to a better
appreciation of these violations of the FDT, as well as certain consequent
modifications to the concept of an effective temperature.Comment: 15pages, 17figure
Fluctuations of the total entropy production in stochastic systems
Fluctuations of the excess heat in an out of equilibrium steady state are
experimentally investigated in two stochastic systems : an electric circuit
with an imposed mean current and a harmonic oscillator driven out of
equilibrium by a periodic torque. In these two linear systems, we study excess
heat that represents the difference between the dissipated heat out of
equilibrium and the dissipated heat at equilibrium. Fluctuation theorem holds
for the excess heat in the two experimental systems for all observation times
and for all fluctuation magnitudes.Comment: 6
An update on nonequilibrium linear response
The unique fluctuation-dissipation theorem for equilibrium stands in contrast
with the wide variety of nonequilibrium linear response formulae. Their most
traditional approach is "analytic", which, in the absence of detailed balance,
introduces the logarithm of the stationary probability density as observable.
The theory of dynamical systems offers an alternative with a formula that
continues to work when the stationary distribution is not smooth. We show that
this method works equally well for stochastic dynamics, and we illustrate it
with a numerical example for the perturbation of circadian cycles. A second
"probabilistic" approach starts from dynamical ensembles and expands the
probability weights on path space. This line suggests new physical questions,
as we meet the frenetic contribution to linear response, and the relevance of
the change in dynamical activity in the relaxation to a (new) nonequilibrium
condition.Comment: v2: removed typos, updated ref
Time scales and exponential trends to equilibrium: Gaussian model problems
We review results on the exponential convergence of multi- dimensional Ornstein-Uhlenbeck processes and discuss related notions of characteristic timescales with concrete model systems. We focus, on the one hand, on exit time distributions and provide ecplicit expressions for the exponential rate of the distribution in the small noise limit. On the other hand, we consider relaxation timescales of the process to its equi- librium measured in terms of relative entropy and discuss the connection with exit probabilities. Along these lines, we study examples which il- lustrate specific properties of the relaxation and discuss the possibility of deriving a simulation-based, empirical definition of slow and fast de- grees of freedom which builds upon a partitioning of the relative entropy functional in conjuction with the observed relaxation behaviour
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