195 research outputs found
Variational formula for experimental determination of high-order correlations of current fluctuations in driven systems
For Brownian motion of a single particle subject to a tilted periodic
potential on a ring, we propose a formula for experimentally determining the
cumulant generating function of time-averaged current without measurements of
current fluctuations. We first derive this formula phenomenologically on the
basis of two key relations: a fluctuation relation associated with Onsager's
principle of the least energy dissipation in a sufficiently local region and an
additivity relation by which spatially inhomogeneous fluctuations can be
properly considered. We then derive the formula without any phenomenological
assumptions. We also demonstrate its practical advantage by numerical
experiments.Comment: 4 pages, 1 figure; In ver. 2, the organization of the paper has been
revised. In ver. 3, substantial revisions have been don
Finite-Size Scaling of a First-Order Dynamical Phase Transition: Adaptive Population Dynamics and an Effective Model
We analyze large deviations of the time-averaged activity in the one
dimensional Fredrickson-Andersen model, both numerically and analytically. The
model exhibits a dynamical phase transition, which appears as a singularity in
the large deviation function. We analyze the finite-size scaling of this phase
transition numerically, by generalizing an existing cloning algorithm to
include a multi-canonical feedback control: this significantly improves the
computational efficiency. Motivated by these numerical results, we formulate an
effective theory for the model in the vicinity of the phase transition, which
accounts quantitatively for the observed behavior. We discuss potential
applications of the numerical method and the effective theory in a range of
more general contexts.Comment: 20 pages, 10 figure
Finite-time and finite-size scalings in the evaluation of large-deviation functions: Analytical study using a birth-death process
The Giardin\`a-Kurchan-Peliti algorithm is a numerical procedure that uses
population dynamics in order to calculate large deviation functions associated
to the distribution of time-averaged observables. To study the numerical errors
of this algorithm, we explicitly devise a stochastic birth-death process that
describes the time evolution of the population probability. From this
formulation, we derive that systematic errors of the algorithm decrease
proportionally to the inverse of the population size. Based on this
observation, we propose a simple interpolation technique for the better
estimation of large deviation functions. The approach we present is detailed
explicitly in a two-state model.Comment: 13 pages, 1 figure. First part of pair of companion papers, Part II
being arXiv:1607.0880
Rare transitions to thin-layer turbulent condensates
Turbulent flows in a thin layer can develop an inverse energy cascade leading
to spectral condensation of energy when the layer height is smaller than a
certain threshold. These spectral condensates take the form of large-scale
vortices in physical space. Recently, evidence for bistability was found in
this system close to the critical height: depending on the initial conditions,
the flow is either in a condensate state with most of the energy in the
two-dimensional (2-D) large-scale modes, or in a three-dimensional (3-D) flow
state with most of the energy in the small-scale modes. This bistable regime is
characterised by the statistical properties of random and rare transitions
between these two locally stable states. Here, we examine these statistical
properties in thin-layer turbulent flows, where the energy is injected by
either stochastic or deterministic forcing. To this end, by using a large
number of direct numerical simulations (DNS), we measure the decay time
of the 2-D condensate to 3-D flow state and the build-up time
of the 2-D condensate. We show that both of these times follow
an exponential distribution with mean values increasing faster than
exponentially as the layer height approaches the threshold. We further show
that the dynamics of large-scale kinetic energy may be modeled by a stochastic
Langevin equation. From time-series analysis of DNS data, we determine the
effective potential that shows two minima corresponding to the 2-D and 3-D
states when the layer height is close to the threshold
How dissipation constrains fluctuations in nonequilibrium liquids: Diffusion, structure and biased interactions
The dynamics and structure of nonequilibrium liquids, driven by
non-conservative forces which can be either external or internal, generically
hold the signature of the net dissipation of energy in the thermostat. Yet,
disentangling precisely how dissipation changes collective effects remains
challenging in many-body systems due to the complex interplay between driving
and particle interactions. First, we combine explicit coarse-graining and
stochastic calculus to obtain simple relations between diffusion, density
correlations and dissipation in nonequilibrium liquids. Based on these results,
we consider large-deviation biased ensembles where trajectories mimic the
effect of an external drive. The choice of the biasing function is informed by
the connection between dissipation and structure derived in the first part.
Using analytical and computational techniques, we show that biasing
trajectories effectively renormalizes interactions in a controlled manner, thus
providing intuition on how driving forces can lead to spatial organization and
collective dynamics. Altogether, our results show how tuning dissipation
provides a route to alter the structure and dynamics of liquids and soft
materials.Comment: 21 pages, 7 figure
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