581 research outputs found
Entropic aging and extreme value statistics
Entropic aging consists in a progressive slowing down of the low-temperature
dynamics of a glassy system due to the rarefaction of downwards directions on
the energy landscape, as lower and lower energy levels are reached. A
prototypical model exhibiting this scenario is the Barrat-M\'ezard model. We
argue that in the zero-temperature limit, this model precisely corresponds to a
dynamical realization of extreme value statistics, providing an interesting
connection between the two fields. This mapping directly yields the long-time
asymptotic shape of the dynamical energy distribution, which is then one of the
standard extreme value distributions (Gumbel, Weibull or Fr\'echet), thus
restricting the class of asymptotic energy distributions with respect to the
original preasymptotic results. We also briefly discuss similarities and
differences between the Barrat-M\'ezard model and undriven dissipative systems
like granular gases.Comment: 8 pages, to appear in J. Phys.
Participation ratio for constraint-driven condensation with superextensive mass
Broadly distributed random variables with a power-law distribution are known to generate condensation effects, in the sense that,
when the exponent lies in a certain interval, the largest variable in
a sum of (independent and identically distributed) terms is for large
of the same order as the sum itself. In particular, when the distribution has
infinite mean () one finds unconstrained condensation, whereas for
constrained condensation takes places fixing the total mass to a
large enough value . In both cases, a standard
indicator of the condensation phenomenon is the participation ratio
(), which takes a
finite value for when condensation occurs. To better understand
the connection between constrained and unconstrained condensation, we study
here the situation when the total mass is fixed to a superextensive value (), hence interpolating between the unconstrained
condensation case (where the typical value of the total mass scales as for ) and the extensive constrained mass. In particular
we show that for exponents is separated from a homogeneous phase at by a transition line, , where a weak condensation
phenomenon takes place. We focus on the evaluation of the participation ratio
as a generic indicator of condensation, also recalling or presenting results in
the standard cases of unconstrained mass and of fixed extensive mass.Comment: 11 pages, 2 figures, to appear in Entrop
The glass transition in a nutshell: a source of inspiration to describe the subcritical transition to turbulence
The starting point of the present work is the observation of possible
analogies, both at the phenomenological and at the methodological level,
between the subcritical transition to turbulence and the glass transition.
Having recalled the phenomenology of the subcritical transition to turbulence,
we review the theories of the glass transition at a very basic level, focusing
on the history of their development as well as on the concepts they have
elaborated. Doing so, we aim at attracting the attention on the above mentioned
analogies, which we believe could inspire new developments in the theory of the
subcritical transition to turbulence. We then briefly describe a model inspired
by one of the simplest and most inspiring model of the glass transition, the
so-called Random Energy Model, as a first step in that direction.Comment: 9 pages, 1 figure; to appear in a topical issue of Eur. Phys. J. E
dedicated to Paul Mannevill
Dynamical fluctuations in a simple housing market model
We consider a simple stochastic model of a urban rental housing market, in
which the interaction of tenants and landlords induces rent fluctuations. We
simulate the model numerically and measure the equilibrium rent distribution,
which is found to be close to a lognormal law. We also study the influence of
the density of agents (or equivalently, the vacancy rate) on the rent
distribution. A simplified version of the model, amenable to analytical
treatment, is studied and leads to a lognormal distribution of rents. The
predicted equilibrium value agrees quantitatively with numerical simulations,
while a qualitative agreement is obtained for the standard deviation. The
connection with non-equilibrium statistical physics models like ratchets is
also emphasized.Comment: 12 pages, 5 figures, to appear in J. Stat. Mec
Aging of the frictional properties induced by temperature variations
The dry frictional contact between two solid surfaces is well-known to obey
Coulomb friction laws. In particular, the static friction force resisting the
relative lateral (tangential) motion of solid surfaces, initially at rest, is
known to be proportional to the normal force and independent of the area of the
macroscopic surfaces in contact. Experimentally, the static friction force has
been observed to slightly depend on time. Such an aging phenomenon has been
accounted for either by the creep of the material or by the condensation of
water bridges at the microscopic contacts points. Studying a toy-model, we show
that the small uncontrolled temperature changes of the system can also lead to
a significant increase of the static friction force.Comment: 8 pages, 5 figures, final version, to appear in Phys. Rev.
Symmetry-breaking phase transition in a dynamical decision model
We consider a simple decision model in which a set of agents randomly choose
one of two competing shops selling the same perishable products (typically
food). The satisfaction of agents with respect to a given store is related to
the freshness of the previously bought products. Agents select with a higher
probability the store they are most satisfied with. Studying the model from a
statistical physics perspective, both through numerical simulations and
mean-field analytical methods, we find a rich behaviour with continuous and
discontinuous phase transitions between a symmetric phase where both stores
maintain the same level of activity, and a phase with broken symmetry where one
of the two shops attracts more customers than the other.Comment: 13 pages, 6 figures, submitted to JSTA
Statistics of sums of correlated variables described by a matrix product ansatz
We determine the asymptotic distribution of the sum of correlated variables
described by a matrix product ansatz with finite matrices, considering
variables with finite variances. In cases when the correlation length is
finite, the law of large numbers is obeyed, and the rescaled sum converges to a
Gaussian distribution. In constrast, when correlation extends over system size,
we observe either a breaking of the law of large numbers, with the onset of
giant fluctuations, or a generalization of the central limit theorem with a
family of nonstandard limit distributions. The corresponding distributions are
found as mixtures of delta functions for the generalized law of large numbers,
and as mixtures of Gaussian distributions for the generalized central limit
theorem. Connections with statistical physics models are emphasized.Comment: 6 pages, 1 figur
Matrix product representation and synthesis for random vectors: Insight from statistical physics
Inspired from modern out-of-equilibrium statistical physics models, a matrix
product based framework permits the formal definition of random vectors (and
random time series) whose desired joint distributions are a priori prescribed.
Its key feature consists of preserving the writing of the joint distribution as
the simple product structure it has under independence, while inputing
controlled dependencies amongst components: This is obtained by replacing the
product of distributions by a product of matrices of distributions. The
statistical properties stemming from this construction are studied
theoretically: The landscape of the attainable dependence structure is
thoroughly depicted and a stationarity condition for time series is notably
obtained. The remapping of this framework onto that of Hidden Markov Models
enables us to devise an efficient and accurate practical synthesis procedure. A
design procedure is also described permitting the tuning of model parameters to
attain targeted properties. Pedagogical well-chosen examples of times series
and multivariate vectors aim at illustrating the power and versatility of the
proposed approach and at showing how targeted statistical properties can be
actually prescribed.Comment: 10 pages, 4 figures, submitted to IEEE Transactions on Signal
Processin
Dependence of the fluctuation-dissipation temperature on the choice of observable
On general grounds, a nonequilibrium temperature can be consistently defined
from generalized fluctuation-dissipation relations only if it is independent of
the observable considered. We argue that the dependence on the choice of
observable generically occurs when the phase-space probability distribution is
non-uniform on constant energy shells. We relate quantitatively this observable
dependence to a fundamental characteristics of nonequilibrium systems, namely
the Shannon entropy difference with respect to the equilibrium state with the
same energy. This relation is illustrated on a mean-field model in contact with
two heat baths at different temperatures.Comment: 4 pages, 2 figures, final versio
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