256 research outputs found
Fluctuation relation for a L\'evy particle
We study the work fluctuations of a particle subjected to a deterministic
drag force plus a random forcing whose statistics is of the L\'evy type. In the
stationary regime, the probability density of the work is found to have ``fat''
power-law tails which assign a relatively high probability to large
fluctuations compared with the case where the random forcing is Gaussian. These
tails lead to a strong violation of existing fluctuation theorems, as the ratio
of the probabilities of positive and negative work fluctuations of equal
magnitude behaves in a non-monotonic way. Possible experiments that could probe
these features are proposed.Comment: 5 pages, 2 figures, RevTeX4; v2: minor corrections and references
added; v3: typos corrected, new conclusion, close to published versio
Brownian motion with dry friction: Fokker-Planck approach
We solve a Langevin equation, first studied by de Gennes, in which there is a
solid-solid or dry friction force acting on a Brownian particle in addition to
the viscous friction usually considered in the study of Brownian motion. We
obtain both the time-dependent propagator of this equation and the velocity
correlation function by solving the associated time-dependent Fokker-Planck
equation. Exact results are found for the case where only dry friction acts on
the particle. For the case where both dry and viscous friction forces are
present, series representations of the propagator and correlation function are
obtained in terms of parabolic cylinder functions. Similar series
representations are also obtained for the case where an external constant force
is added to the Langevin equation.Comment: 18 pages, 13 figures (in color
Path integral approach to random motion with nonlinear friction
Using a path integral approach, we derive an analytical solution of a
nonlinear and singular Langevin equation, which has been introduced previously
by P.-G. de Gennes as a simple phenomenological model for the stick-slip motion
of a solid object on a vibrating horizontal surface. We show that the optimal
(or most probable) paths of this model can be divided into two classes of
paths, which correspond physically to a sliding or slip motion, where the
object moves with a non-zero velocity over the underlying surface, and a
stick-slip motion, where the object is stuck to the surface for a finite time.
These two kinds of basic motions underlie the behavior of many more complicated
systems with solid/solid friction and appear naturally in de Gennes' model in
the path integral framework.Comment: 18 pages, 3 figure
Superstatistics, thermodynamics, and fluctuations
A thermodynamic-like formalism is developed for superstatistical systems
based on conditional entropies. This theory takes into account large-scale
variations of intensive variables of systems in nonequilibrium stationary
states. Ordinary thermodynamics is recovered as a special case of the present
theory, and corrections to it can be systematically evaluated. A generalization
of Einstein's relation for fluctuations is presented using a maximum entropy
condition.Comment: 16 pages, no figures. The title changed, some explanations and
references added. Accepted for publication in Phys. Rev.
Stick-slip motion of solids with dry friction subject to random vibrations and an external field
We investigate a model for the dynamics of a solid object, which moves over a
randomly vibrating solid surface and is subject to a constant external force.
The dry friction between the two solids is modeled phenomenologically as being
proportional to the sign of the object's velocity relative to the surface, and
therefore shows a discontinuity at zero velocity. Using a path integral
approach, we derive analytical expressions for the transition probability of
the object's velocity and the stationary distribution of the work done on the
object due to the external force. From the latter distribution, we also derive
a fluctuation relation for the mechanical work fluctuations, which incorporates
the effect of the dry friction.Comment: v1: 23 pages, 9 figures; v2: Reference list corrected; v3: Published
version, typos corrected, references adde
The Value of Information for Populations in Varying Environments
The notion of information pervades informal descriptions of biological
systems, but formal treatments face the problem of defining a quantitative
measure of information rooted in a concept of fitness, which is itself an
elusive notion. Here, we present a model of population dynamics where this
problem is amenable to a mathematical analysis. In the limit where any
information about future environmental variations is common to the members of
the population, our model is equivalent to known models of financial
investment. In this case, the population can be interpreted as a portfolio of
financial assets and previous analyses have shown that a key quantity of
Shannon's communication theory, the mutual information, sets a fundamental
limit on the value of information. We show that this bound can be violated when
accounting for features that are irrelevant in finance but inherent to
biological systems, such as the stochasticity present at the individual level.
This leads us to generalize the measures of uncertainty and information usually
encountered in information theory
Development and aetiology of body dissatisfaction in adolescent boys and girls
This longitudinal study aims to describe the development of body dissatisfaction (BD), measured with the Contour Drawing Rating Scale, between the ages of 14 and 18, and to identify factors associated with BD at age 18, among 413 adolescents. Between the ages of 14 and 18, the proportion of girls wanting to be thinner increased, although it remained unchanged among boys. A ratio of 1:2 girls and 1:5 boys reported having seriously tried to lose weight. Factors associated with BD in girls at age 18 were (1) wanting to be thinner, (2) body mass index (BMI), (3) weight control behaviours and (4) negative comments about weight. Factors associated with BD in boys at age 18 were (1) wanting to be thinner or bigger, (2) BMI, (3) having experienced sexual intercourse and (4) negative comments about weight. The high prevalence of BD and weight-related concerns suggest a need for early interventions. © 2014 © 2014 The Author(s). Published by Taylor & Francis
Counting function fluctuations and extreme value threshold in multifractal patterns: the case study of an ideal noise
To understand the sample-to-sample fluctuations in disorder-generated
multifractal patterns we investigate analytically as well as numerically the
statistics of high values of the simplest model - the ideal periodic
Gaussian noise. By employing the thermodynamic formalism we predict the
characteristic scale and the precise scaling form of the distribution of number
of points above a given level. We demonstrate that the powerlaw forward tail of
the probability density, with exponent controlled by the level, results in an
important difference between the mean and the typical values of the counting
function. This can be further used to determine the typical threshold of
extreme values in the pattern which turns out to be given by
with . Such observation provides a
rather compelling explanation of the mechanism behind universality of .
Revealed mechanisms are conjectured to retain their qualitative validity for a
broad class of disorder-generated multifractal fields. In particular, we
predict that the typical value of the maximum of intensity is to be
given by , where is the
corresponding singularity spectrum vanishing at . For the
noise we also derive exact as well as well-controlled approximate
formulas for the mean and the variance of the counting function without
recourse to the thermodynamic formalism.Comment: 28 pages; 7 figures, published version with a few misprints
corrected, editing done and references adde
Universal quantum interfaces
To observe or control a quantum system, one must interact with it via an
interface. This letter exhibits simple universal quantum interfaces--quantum
input/output ports consisting of a single two-state system or quantum bit that
interacts with the system to be observed or controlled. It is shown that under
very general conditions the ability to observe and control the quantum bit on
its own implies the ability to observe and control the system itself. The
interface can also be used as a quantum communication channel, and multiple
quantum systems can be connected by interfaces to become an efficient universal
quantum computer. Experimental realizations are proposed, and implications for
controllability, observability, and quantum information processing are
explored.Comment: 4 pages, 3 figures, RevTe
Nonconcave entropies in multifractals and the thermodynamic formalism
We discuss a subtlety involved in the calculation of multifractal spectra
when these are expressed as Legendre-Fenchel transforms of functions analogous
to free energy functions. We show that the Legendre-Fenchel transform of a free
energy function yields the correct multifractal spectrum only when the latter
is wholly concave. If the spectrum has no definite concavity, then the
transform yields the concave envelope of the spectrum rather than the spectrum
itself. Some mathematical and physical examples are given to illustrate this
result, which lies at the root of the nonequivalence of the microcanonical and
canonical ensembles. On a more positive note, we also show that the
impossibility of expressing nonconcave multifractal spectra through
Legendre-Fenchel transforms of free energies can be circumvented with the help
of a generalized free energy function, which relates to a recently introduced
generalized canonical ensemble. Analogies with the calculation of rate
functions in large deviation theory are finally discussed.Comment: 9 pages, revtex4, 3 figures. Changes in v2: sections added on
applications plus many new references; contains an addendum not contained in
published versio
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