51 research outputs found
On anomalous diffusion and the out of equilibrium response function in one-dimensional models
We study how the Einstein relation between spontaneous fluctuations and the
response to an external perturbation holds in the absence of currents, for the
comb model and the elastic single-file, which are examples of systems with
subdiffusive transport properties. The relevance of non-equilibrium conditions
is investigated: when a stationary current (in the form of a drift or an energy
flux) is present, the Einstein relation breaks down, as is known to happen in
systems with standard diffusion. In the case of the comb model, a general
relation, which has appeared in the recent literature, between the response
function and an unperturbed suitable correlation function, allows us to explain
the observed results. This suggests that a relevant ingredient in breaking the
Einstein formula, for stationary regimes, is not the anomalous diffusion but
the presence of currents driving the system out of equilibrium.Comment: 10 pages, 4 figure
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
Irreversible effects of memory
The steady state of a Langevin equation with short ranged memory and coloured
noise is analyzed. When the fluctuation-dissipation theorem of second kind is
not satisfied, the dynamics is irreversible, i.e. detailed balance is violated.
We show that the entropy production rate for this system should include the
power injected by ``memory forces''. With this additional contribution, the
Fluctuation Relation is fairly verified in simulations. Both dynamics with
inertia and overdamped dynamics yield the same expression for this additional
power. The role of ``memory forces'' within the fluctuation-dissipation
relation of first kind is also discussed.Comment: 6 pages, 1 figure, publishe
The deactivation of an NH3-SCR Cu-SAPO catalyst upon exposure to non-oxidizing conditions
Abstract A Cu-SAPO catalyst for NH3-SCR applications showed a significant loss of deNOx performance after exposure to oxygen-free conditions. The present work aims at elucidating the causes of the observed progressive deactivation by comparing different experimental procedures for the SCR activity tests. The adoption of an experimental protocol, which avoids the exposure to a non-oxidizing environment, ensured a stable activity of the Cu-SAPO catalyst. Moreover, treatment of the deactivated catalyst with an oxidizing mixture at 550 °C for 5 h enabled to partially recover the deNOx activity
Non-equilibrium and information: the role of cross-correlations
We discuss the relevance of information contained in cross-correlations among
different degrees of freedom, which is crucial in non-equilibrium systems. In
particular we consider a stochastic system where two degrees of freedom
and - in contact with two different thermostats - are coupled together.
The production of entropy and the violation of equilibrium
fluctuation-dissipation theorem (FDT) are both related to the cross-correlation
between and . Information about such cross-correlation may be lost
when single-variable reduced models, for , are considered. Two different
procedures are typically applied: (a) one totally ignores the coupling with
; (b) one models the effect of as an average memory effect,
obtaining a generalized Langevin equation. In case (a) discrepancies between
the system and the model appear both in entropy production and linear response;
the latter can be exploited to define effective temperatures, but those are
meaningful only when time-scales are well separated. In case (b) linear
response of the model well reproduces that of the system; however the loss of
information is reflected in a loss of entropy production. When only linear
forces are present, such a reduction is dramatic and makes the average entropy
production vanish, posing problems in interpreting FDT violations.Comment: 30 pages, 4 figures, 4 appendixe
Harmonic damped oscillators with feedback. A Langevin study
We consider a system in direct contact with a thermal reservoir and which, if
left unperturbed, is well described by a memory-less equilibrium Langevin
equation of the second order in the time coordinate. In such conditions, the
strength of the noise fluctuations is set by the damping factor, in accordance
with the Fluctuation and Dissipation theorem. We study the system when it is
subject to a feedback mechanism, by modifying the Langevin equation
accordingly. Memory terms now arise in the time evolution, which we study in a
non-equilibrium steady state. Two types of feedback schemes are considered, one
focusing on time shifts and one on phase shifts, and for both cases we evaluate
the power spectrum of the system's fluctuations. Our analysis finds application
in feedback cooled oscillators, such as the Gravitational Wave detector AURIGA.Comment: 17 page
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
Effective temperatures of a heated Brownian particle
We investigate various possible definitions of an effective temperature for a
particularly simple nonequilibrium stationary system, namely a heated Brownian
particle suspended in a fluid. The effective temperature based on the
fluctuation dissipation ratio depends on the time scale under consideration, so
that a simple Langevin description of the heated particle is impossible. The
short and long time limits of this effective temperature are shown to be
consistent with the temperatures estimated from the kinetic energy and Einstein
relation, respectively. The fluctuation theorem provides still another
definition of the temperature, which is shown to coincide with the short time
value of the fluctuation dissipation ratio
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
Granular Brownian motion
We study the stochastic motion of an intruder in a dilute driven granular
gas. All particles are coupled to a thermostat, representing the external
energy source, which is the sum of random forces and a viscous drag. The
dynamics of the intruder, in the large mass limit, is well described by a
linear Langevin equation, combining the effects of the external bath and of the
"granular bath". The drag and diffusion coefficients are calculated under few
assumptions, whose validity is well verified in numerical simulations. We also
discuss the non-equilibrium properties of the intruder dynamics, as well as the
corrections due to finite packing fraction or finite intruder mass.Comment: 19 pages, 4 figures, in press on Journal of Statistical Mechanics:
Theory and Experiment
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