228 research outputs found
Nonequilibrium fluctuation-dissipation theorem and heat production
We use a relationship between response and correlation function in
nonequilibrium systems to establish a connection between the heat production
and the deviations from the equilibrium fluctuation-dissipation theorem. This
scheme extends the Harada-Sasa formulation [Phys. Rev. Lett. 95, 130602
(2005)], obtained for Langevin equations in steady states, as it also holds for
transient regimes and for discrete jump processes involving small entropic
changes. Moreover, a general formulation includes two times and the new
concepts of two-time work, kinetic energy, and of a two-time heat exchange that
can be related to a nonequilibrium "effective temperature". Numerical
simulations of a chain of anharmonic oscillators and of a model for a molecular
motor driven by ATP hydrolysis illustrate these points.Comment: 5 pages, 3 figure
Heat fluctuations of Brownian oscillators in nonstationary processes: fluctuation theorem and condensation transition
We study analytically the probability distribution of the heat released by an
ensemble of harmonic oscillators to the thermal bath, in the nonequilibrium
relaxation process following a temperature quench. We focus on the asymmetry
properties of the heat distribution in the nonstationary dynamics, in order to
study the forms taken by the Fluctuation Theorem as the number of degrees of
freedom is varied. After analysing in great detail the cases of one and two
oscillators, we consider the limit of a large number of oscillators, where the
behavior of fluctuations is enriched by a condensation transition with a
nontrivial phase diagram, characterized by reentrant behavior. Numerical
simulations confirm our analytical findings. We also discuss and highlight how
concepts borrowed from the study of fluctuations in equilibrium under symmetry
breaking conditions [Gaspard, J. Stat. Mech. P08021 (2012)] turn out to be
quite useful in understanding the deviations from the standard Fluctuation
Theorem.Comment: 16 pages, 7 figure
Induced and endogenous acoustic oscillations in granular faults
The frictional properties of disordered systems are affected by external
perturbations. These perturbations usually weaken the system by reducing the
macroscopic friction coefficient. This friction reduction is of particular
interest in the case of disordered systems composed of granular particles
confined between two plates, as this is a simple model of seismic fault.
Indeed, in the geophysical context frictional weakening could explain the
unexpected weakness of some faults, as well as earthquake remote triggering. In
this manuscript we review recent results concerning the response of confined
granular systems to external perturbations, considering the different
mechanisms by which the perturbation could weaken a system, the relevance of
the frictional reduction to earthquakes, as well as discussing the intriguing
scenario whereby the weakening is not monotonic in the perturbation frequency,
so that a re-entrant transition is observed, as the system first enters a
fluidized state and then returns to a frictional state.Comment: 15 pages, 12 figure
Nonlinear susceptibilities and the measurement of a cooperative length
We derive the exact beyond-linear fluctuation dissipation relation,
connecting the response of a generic observable to the appropriate correlation
functions, for Markov systems. The relation, which takes a similar form for
systems governed by a master equation or by a Langevin equation, can be derived
to every order, in large generality with respect to the considered model, in
equilibrium and out of equilibrium as well. On the basis of the fluctuation
dissipation relation we propose a particular response function, namely the
second order susceptibility of the two-particle correlation function, as an
effective quantity to detect and quantify cooperative effects in glasses and
disordered systems. We test this idea by numerical simulations of the
Edwards-Anderson model in one and two dimensions.Comment: 5 pages, 2 figure
Questioning the tension via the look-back time
The Hubble tension is investigated taking into account the cosmological
look-back time. Specifically, considering a single equation, widely used in
standard cosmology, it is possible to recover both values of the Hubble
constant reported by the SH0ES and Planck collaborations: the former is
obtained through cosmological ladder methods (e.g. Cepheids, Supernovae Type
IA) and the latter through measurements of the Cosmic Microwave Background.
Also, other values obtained in the literature are achieved with the same
approach. We conclude that the Hubble tension can be removed if the look-back
time is correctly referred to the redshift where the measurement is performed.Comment: 8 pages, 1 figure, accepted for publication in Physics of the Dark
Univers
Fluctuating hydrodynamics and correlation lengths in a driven granular fluid
Static and dynamical structure factors for shear and longitudinal modes of
the velocity and density fields are computed for a granular system fluidized by
a stochastic bath with friction. Analytical expressions are obtained through
fluctuating hydrodynamics and are successfully compared with numerical
simulations up to a volume fraction . Hydrodynamic noise is the sum
of external noise due to the bath and internal one due to collisions. Only the
latter is assumed to satisfy the fluctuation-dissipation relation with the
average granular temperature. Static velocity structure factors
and display a general non-constant behavior with two plateaux
at large and small , representing the granular temperature and the
bath temperature respectively. From this behavior, two different
velocity correlation lengths are measured, both increasing as the packing
fraction is raised. This growth of spatial order is in agreement with the
behaviour of dynamical structure factors, the decay of which becomes slower and
slower at increasing density.Comment: 24 pages, 8 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
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