730 research outputs found
A numerical approach to large deviations in continuous-time
We present an algorithm to evaluate the large deviation functions associated
to history-dependent observables. Instead of relying on a time discretisation
procedure to approximate the dynamics, we provide a direct continuous-time
algorithm, valuable for systems with multiple time scales, thus extending the
work of Giardin\`a, Kurchan and Peliti (PRL 96, 120603 (2006)).
The procedure is supplemented with a thermodynamic-integration scheme, which
improves its efficiency. We also show how the method can be used to probe large
deviation functions in systems with a dynamical phase transition -- revealed in
our context through the appearance of a non-analyticity in the large deviation
functions.Comment: Submitted to J. Stat. Mec
Irreversibility in a simple reversible model
This paper studies a parametrized family of familiar generalized baker maps,
viewed as simple models of time-reversible evolution. Mapping the unit square
onto itself, the maps are partly contracting and partly expanding, but they
preserve the global measure of the definition domain. They possess periodic
orbits of any period, and all maps of the set have attractors with well defined
structure. The explicit construction of the attractors is described and their
structure is studied in detail. There is a precise sense in which one can speak
about absolute age of a state, regardless of whether the latter is applied to a
single point, a set of points, or a distribution function. One can then view
the whole trajectory as a set of past, present and future states. This
viewpoint is then applied to show that it is impossible to define a priori
states with very large "negative age". Such states can be defined only a
posteriori. This gives precise sense to irreversibility -- or the "arrow of
time" -- in these time-reversible maps, and is suggested as an explanation of
the second law of thermodynamics also for some realistic physical systems.Comment: 15 pages, 12 Postscript figure
An Extension of the Fluctuation Theorem
Heat fluctuations are studied in a dissipative system with both mechanical
and stochastic components for a simple model: a Brownian particle dragged
through water by a moving potential. An extended stationary state fluctuation
theorem is derived. For infinite time, this reduces to the conventional
fluctuation theorem only for small fluctuations; for large fluctuations, it
gives a much larger ratio of the probabilities of the particle to absorb rather
than supply heat. This persists for finite times and should be observable in
experiments similar to a recent one of Wang et al.Comment: 12 pages, 1 eps figure in color (though intelligible in black and
white
Fluctuations of the heat flux of a one-dimensional hard particle gas
Momentum-conserving one-dimensional models are known to exhibit anomalous
Fourier's law, with a thermal conductivity varying as a power law of the system
size. Here we measure, by numerical simulations, several cumulants of the heat
flux of a one-dimensional hard particle gas. We find that the cumulants, like
the conductivity, vary as power laws of the system size. Our results also
indicate that cumulants higher than the second follow different power laws when
one compares the ring geometry at equilibrium and the linear case in contact
with two heat baths (at equal or unequal temperatures). keywords: current
fluctuations, anomalous Fourier law, hard particle gasComment: 5 figure
Free Energy Functional for Nonequilibrium Systems: An Exactly Solvable Case
We consider the steady state of an open system in which there is a flux of
matter between two reservoirs at different chemical potentials. For a large
system of size , the probability of any macroscopic density profile
is ; thus generalizes to
nonequilibrium systems the notion of free energy density for equilibrium
systems. Our exact expression for is a nonlocal functional of ,
which yields the macroscopically long range correlations in the nonequilibrium
steady state previously predicted by fluctuating hydrodynamics and observed
experimentally.Comment: 4 pages, RevTeX. Changes: correct minor errors, add reference, minor
rewriting requested by editors and refere
Domino tilings and the six-vertex model at its free fermion point
At the free-fermion point, the six-vertex model with domain wall boundary
conditions (DWBC) can be related to the Aztec diamond, a domino tiling problem.
We study the mapping on the level of complete statistics for general domains
and boundary conditions. This is obtained by associating to both models a set
of non-intersecting lines in the Lindstroem-Gessel-Viennot (LGV) scheme. One of
the consequence for DWBC is that the boundaries of the ordered phases are
described by the Airy process in the thermodynamic limit.Comment: 14 pages, 8 figure
On the Fibonacci universality classes in nonlinear fluctuating hydrodynamics
We present a lattice gas model that without fine tuning of parameters is
expected to exhibit the so far elusive modified Kardar-Parisi-Zhang (KPZ)
universality class. To this end, we review briefly how non-linear fluctuating
hydrodynamics in one dimension predicts that all dynamical universality classes
in its range of applicability belong to an infinite discrete family which we
call Fibonacci family since their dynamical exponents are the Kepler ratios
of neighbouring Fibonacci numbers , including
diffusion (), KPZ (), and the limiting ratio which is the
golden mean . Then we revisit the case of two
conservation laws to which the modified KPZ model belongs. We also derive
criteria on the macroscopic currents to lead to other non-KPZ universality
classes.Comment: 17 page
On the master equation approach to kinetic theory: linear and nonlinear Fokker--Planck equations
We discuss the relationship between kinetic equations of the Fokker-Planck
type (two linear and one non-linear) and the Kolmogorov (a.k.a. master)
equations of certain N-body diffusion processes, in the context of Kac's
"propagation of chaos" limit. The linear Fokker-Planck equations are
well-known, but here they are derived as a limit N->infty of a simple linear
diffusion equation on (3N-C)-dimensional N-velocity spheres of radius sqrt(N)
(with C=1 or 4 depending on whether the system conserves energy only or energy
and momentum). In this case, a spectral gap separating the zero eigenvalue from
the positive spectrum of the Laplacian remains as N->infty,so that the
exponential approach to equilibrium of the master evolution is passed on to the
limiting Fokker-Planck evolution in R^3. The non-linear Fokker-Planck equation
is known as Landau's equation in the plasma physics literature. Its N-particle
master equation, originally introduced (in the 1950s) by Balescu and Prigogine
(BP), is studied here on the (3N-4)-dimensional N-velocity sphere. It is shown
that the BP master equation represents a superposition of diffusion processes
on certain two-dimensional sub-manifolds of R^{3N} determined by the
conservation laws for two-particle collisions. The initial value problem for
the BP master equation is proved to be well-posed and its solutions are shown
to decay exponentially fast to equilibrium. However, the first non-zero
eigenvalue of the BP operator is shown to vanish in the limit N->infty. This
indicates that the exponentially fast approach to equilibrium may not be passed
from the finite-N master equation on to Landau's nonlinear kinetic equation.Comment: 20 pages; based on talk at the 18th ICTT Conference. Some typos and a
few minor technical fixes. Modified title slightl
Dynamical large deviations for a boundary driven stochastic lattice gas model with many conserved quantities
We prove the dynamical large deviations for a particle system in which
particles may have different velocities. We assume that we have two infinite
reservoirs of particles at the boundary: this is the so-called boundary driven
process. The dynamics we considered consists of a weakly asymmetric simple
exclusion process with collision among particles having different velocities
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