886 research outputs found
Fluctuations in 2D reversibly-damped turbulence
Gallavotti proposed an equivalence principle in hydrodynamics, which states
that forced-damped fluids can be equally well represented by means of the
Navier-Stokes equations and by means of time reversible dynamical systems
called GNS. In the GNS systems, the usual viscosity is replaced by a
state-dependent dissipation term which fixes one global quantity. The principle
states that the mean values of properly chosen observables are the same for
both representations of the fluid. In the same paper, the chaotic hypothesis of
Gallavotti and Cohen is applied to hydrodynamics, leading to the conjecture
that entropy fluctuations in the GNS system verify a relation first observed in
nonequilibrium molecular dynamics. We tested these ideas in the case of
two-dimensional fluids. We examined the fluctuations of global quadratic
quantities in the statistically stationary state of a) the Navier-Stokes
equations; b) the GNS equations. Our results are consistent with the validity
of the fluctuation relation, and of the equivalence principle, indicating
possible extensions thereof. Moreover, in these results the difference between
the Gallavotti-Cohen fluctuation theorem and the Evans-Searles identity is
evident.Comment: latex-2e, 14 pages, 6 figures, submitted to Nonlinearity. Revised
version following the referees' comments: text polished, a few algebraic
mistakes corrected, figures improved, reference to the Evans-Searles identity
adde
Quantum thermostatted disordered systems and sensitivity under compression
A one-dimensional quantum system with off diagonal disorder, consisting of a
sample of conducting regions randomly interspersed within potential barriers is
considered. Results mainly concerning the large limit are presented. In
particular, the effect of compression on the transmission coefficient is
investigated. A numerical method to simulate such a system, for a physically
relevant number of barriers, is proposed. It is shown that the disordered model
converges to the periodic case as increases, with a rate of convergence
which depends on the disorder degree. Compression always leads to a decrease of
the transmission coefficient which may be exploited to design
nano-technological sensors. Effective choices for the physical parameters to
improve the sensitivity are provided. Eventually large fluctuations and rate
functions are analysed.Comment: 21 pages, 10 figure
About the maximum entropy principle in non equilibrium statistical mechanics
The maximum entropy principle (MEP) apparently allows us to derive, or
justify, fundamental results of equilibrium statistical mechanics. Because of
this, a school of thought considers the MEP as a powerful and elegant way to
make predictions in physics and other disciplines, which constitutes an
alternative and more general method than the traditional ones of statistical
mechanics. Actually, careful inspection shows that such a success is due to a
series of fortunate facts that characterize the physics of equilibrium systems,
but which are absent in situations not described by Hamiltonian dynamics, or
generically in nonequilibrium phenomena. Here we discuss several important
examples in non equilibrium statistical mechanics, in which the MEP leads to
incorrect predictions, proving that it does not have a predictive nature. We
conclude that, in these paradigmatic examples, the "traditional" methods based
on a detailed analysis of the relevant dynamics cannot be avoided
Orbital measures in non-equilibrium statistical mechanics: the Onsager relations
We assume that the properties of nonequilibrium stationary states of systems
of particles can be expressed in terms of weighted orbital measures, i.e.
through periodic orbit expansions. This allows us to derive the Onsager
relations for systems of particles subject to a Gaussian thermostat, under
the assumption that the entropy production rate is equal to the phase space
contraction rate. Moreover, this also allows us to prove that the relevant
transport coefficients are not negative. In the appendix we give an argument
for the proper way of treating grazing collisions, a source of possible
singularities in the dynamics.Comment: LaTeX, 14 pages, 1 TeX figure in the tex
The Gallavotti-Cohen Fluctuation Theorem for a non-chaotic model
We test the applicability of the Gallavotti-Cohen fluctuation formula on a
nonequilibrium version of the periodic Ehrenfest wind-tree model. This is a
one-particle system whose dynamics is rather complex (e.g. it appears to be
diffusive at equilibrium), but its Lyapunov exponents are nonpositive. For
small applied field, the system exhibits a very long transient, during which
the dynamics is roughly chaotic, followed by asymptotic collapse on a periodic
orbit. During the transient, the dynamics is diffusive, and the fluctuations of
the current are found to be in agreement with the fluctuation formula, despite
the lack of real hyperbolicity. These results also constitute an example which
manifests the difference between the fluctuation formula and the Evans-Searles
identity.Comment: 12 pages, submitted to Journal of Statistical Physic
Fluctuation relations for systems in constant magnetic field
The validity of the Fluctuation Relations (FR) for systems in a constant
magnetic field is investigated. Recently introduced time-reversal symmetries
that hold in presence of static electric and magnetic fields and of
deterministic thermostats are used to prove the transient FR without invoking,
as commonly done, inversion of the magnetic field. Steady-state FR are also
derived, under the t-mixing condition. These results extend the predictive
power of important statistical mechanics relations. We illustrate this via the
non-linear response for the cumulants of the dissipation, showing how the new
FR enable to determine analytically null cumulants also for systems in a single
magnetic field.Comment: 1 figure, added reference
Gibbs entropy and irreversible thermodynamics
Recently a number of approaches has been developed to connect the microscopic
dynamics of particle systems to the macroscopic properties of systems in
nonequilibrium stationary states, via the theory of dynamical systems. This way
a direct connection between dynamics and Irreversible Thermodynamics has been
claimed to have been found. However, the main quantity used in these studies is
a (coarse-grained) Gibbs entropy, which to us does not seem suitable, in its
present form, to characterize nonequilibrium states. Various simplified models
have also been devised to give explicit examples of how the coarse-grained
approach may succeed in giving a full description of the Irreversible
Thermodynamics. We analyze some of these models pointing out a number of
difficulties which, in our opinion, need to be overcome in order to establish a
physically relevant connection between these models and Irreversible
Thermodynamics.Comment: 19 pages, 4 eps figures, LaTeX2
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