66 research outputs found
Dynamics of a massive intruder in a homogeneously driven granular fluid
A massive intruder in a homogeneously driven granular fluid, in dilute
configurations, performs a memory-less Brownian motion with drag and
temperature simply related to the average density and temperature of the fluid.
At volume fraction the intruder's velocity correlates with the
local fluid velocity field: such situation is approximately described by a
system of coupled linear Langevin equations equivalent to a generalized
Brownian motion with memory. Here one may verify the breakdown of the
Fluctuation-Dissipation relation and the presence of a net entropy flux - from
the fluid to the intruder - whose fluctuations satisfy the Fluctuation
Relation.Comment: 6 pages, 2 figures, to be published on "Granular Matter" in a special
issue in honor of the memory of Prof. Isaac Goldhirsc
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
Fluctuations in partitioning systems with few degrees of freedom
We study the behavior of a moving wall in contact with a particle gas and
subjected to an external force. We compare the fluctuations of the system
observed in the microcanonical and canonical ensembles, at varying the number
of particles. Static and dynamic correlations signal significant differences
between the two ensembles. Furthermore, velocity-velocity correlations of the
moving wall present a complex two-time relaxation which cannot be reproduced by
a standard Langevin-like description. Quite remarkably, increasing the number
of gas particles in an elongated geometry, we find a typical timescale, related
to the interaction between the partitioning wall and the particles, which grows
macroscopically.Comment: 10 pages, 12 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
Fluctuation-Dissipation relation in sub-diffusive systems: the case of granular single-file
We study a gas of hard rods on a ring, driven by an external thermostat, with
either elastic or inelastic collisions, which exhibits sub-diffusive behavior
. We show the validity of the usual
Fluctuation-Dissipation (FD) relation, i.e. the proportionality between the
response function and the correlation function, when the gas is elastic or
diluted. On the contrary, in strongly inelastic or dense cases, when the tracer
velocity is no more independent of the other degrees of freedom, the Einstein
formula fails and must be replaced by a more general FD relation.Comment: 9 pages, 3 figure
Estimate of temperature and its uncertainty in small systems
The energy of a finite system thermally connected to a thermal reservoir may
fluctuate, while the temperature is a constant representing a thermodynamic
property of the reservoir. The finite system can also be used as a thermometer
for the reservoir. From such a perspective the temperature has an uncertainty,
which can be treated within the framework of estimation theory. We review the
main results of this theory, and clarify some controversial issues regarding
temperature fluctuations. We also offer a simple example of a thermometer with
a small number of particles. We discuss the relevance of the total observation
time, which must be much longer than the decorrelation time
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
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
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