221 research outputs found

### 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 $N$ 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 $N$ 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

### 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

### 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

### 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

### Driven diffusion against electrostatic or effective energy barrier across Alpha-Hemolysin

We analyze the translocation of a charged particle across an Alpha-Hemolysin
(aHL) pore in the framework of a driven diffusion over an extended energy
barrier generated by the electrical charges of the aHL. A one-dimensional
electrostatic potential is extracted from the full 3D solution of the Poisson's
equation. We characterize the particle transport under the action of a constant
forcing by studying the statistics of the translocation time. We derive an
analytical expression of translocation time average that compares well with the
results from Brownian dynamic simulations of driven particles over the
electrostatic potential. Moreover, we show that the translocation time
distributions can be perfectly described by a simple theory which replaces the
true barrier by an equivalent structureless square barrier. Remarkably our
approach maintains its accuracy also for low-applied voltage regimes where the
usual inverse-Gaussian approximation fails. Finally we discuss how the
comparison between the simulated time distributions and their theoretical
prediction results to be greatly simplified when using the notion of the
empirical Laplace transform technique.Comment: RevTeX 4-1, 11 pages, 6 pdf figures, J. Chem. Phys. 2015 in pres

### On the Application of the Gallavotti-Cohen Fluctuation Relation to Thermostatted Steady States Near Equilibrium

The fluctuation relation of the Gallavotti-Cohen Fluctuation Theorem (GCFT)
concerns fluctuations in the phase space compression rate of dissipative,
reversible dynamical systems. It has been proven for Anosov systems, but it is
expected to apply more generally. This raises the question of which non-Anosov
systems satisfy the fluctuation relation. We analyze time dependent
fluctuations in the phase space compression rate of a class of N-particle
systems that are at equilibrium or in near equilibrium steady states. This
class does not include Anosov systems or isoenergetic systems, however, it
includes most steady state systems considered in molecular dynamics simulations
of realistic systems. We argue that the fluctuations of the phase space
compression rate of these systems at or near equilibrium do not satisfy the
fluctuation relation of the GCFT, although the discrepancies become somewhat
smaller as the systems move further from equilibrium. In contrast, similar
fluctuation relations for an appropriately defined dissipation function appear
to hold both near and far from equilibrium.Comment: 46 pages, for publication in PR

### Jarzynski on work and free energy relations: The case of variable volume

Derivations of the Jarzynski equality (JE) appear to be quite general, and applicable to any particle system, whether deterministic or stochastic, under equally general perturbations of an initial equilibrium state at given temperature T. At the same time, the definitions of the quantities appearing in the JE, in particular the work, have been questioned. Answers have been given, but a deeper understanding of the range of phenomena to which the JE applies is necessary, both conceptually and in order to interpret the experiments in which it is used. In fact, domains in which the JE is not applicable have been identified. To clarify the issue, we scrutinize the applicability of the JE to a Hamiltonian particle system in a variable volume. We find that, in this case, the standard interpretation of the terms appearing in the JE is not adequate

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