549 research outputs found
Fluctuations of entropy production in the isokinetic ensemble
We discuss the microscopic definition of entropy production rate in a model
of a dissipative system: a sheared fluid in which the kinetic energy is kept
constant via a Gaussian thermostat. The total phase space contraction rate is
the sum of two statistically independent contributions: the first one is due to
the work of the conservative forces, is independent of the driving force and
does not vanish at zero drive, making the system non-conservative also in
equilibrium. The second is due to the work of the dissipative forces, and is
responsible for the average entropy production; the distribution of its
fluctuations is found to verify the Fluctuation Relation of Gallavotti and
Cohen. The distribution of the fluctuations of the total phase space
contraction rate also verify the Fluctuation Relation. It is compared with the
same quantity calculated in the isoenergetic ensemble: we find that the two
ensembles are equivalent, as conjectured by Gallavotti. Finally, we discuss the
implication of our results for experiments trying to verify the validity of the
FR.Comment: 8 pages, 4 figure
Fluctuation theorem for non-equilibrium relaxational systems driven by external forces
We discuss an extension of the fluctuation theorem to stochastic models that,
in the limit of zero external drive, are not able to equilibrate with their
environment, extending results presented by Sellitto (cond-mat/9809186). We
show that if the entropy production rate is suitably defined, its probability
distribution function verifies the Fluctuation Relation with the ambient
temperature replaced by a (frequency-dependent) effective temperature. We
derive modified Green-Kubo relations. We illustrate these results with the
simple example of an oscillator coupled to a nonequilibrium bath driven by an
external force. We discuss the relevance of our results for driven glasses and
the diffusion of Brownian particles in out of equilibrium media and propose a
concrete experimental strategy to measure the low frequency value of the
effective temperature using the fluctuations of the work done by an ac
conservative field. We compare our results to related ones that appeared in the
literature recently.Comment: 39 pages, 6 figure
Generalized fluctuation relation and effective temperatures in a driven fluid
By numerical simulation of a Lennard-Jones like liquid driven by a velocity
gradient \gamma we test the fluctuation relation (FR) below the (numerical)
glass transition temperature T_g. We show that, in this region, the FR deserves
to be generalized introducing a numerical factor X(T,\gamma)<1 that defines an
``effective temperature'' T_{FR}=T/X. On the same system we also measure the
effective temperature T_{eff}, as defined from the generalized
fluctuation-dissipation relation, and find a qualitative agreement between the
two different nonequilibrium temperatures.Comment: Version accepted for publication on Phys.Rev.E; major changes, 1
figure adde
Saddles and dynamics in a solvable mean-field model
We use the saddle-approach, recently introduced in the numerical
investigation of simple model liquids, in the analysis of a mean-field solvable
system. The investigated system is the k-trigonometric model, a k-body
interaction mean field system, that generalizes the trigonometric model
introduced by Madan and Keyes [J. Chem. Phys. 98, 3342 (1993)] and that has
been recently introduced to investigate the relationship between thermodynamics
and topology of the configuration space. We find a close relationship between
the properties of saddles (stationary points of the potential energy surface)
visited by the system and the dynamics. In particular the temperature
dependence of saddle order follows that of the diffusivity, both having an
Arrhenius behavior at low temperature and a similar shape in the whole
temperature range. Our results confirm the general usefulness of the
saddle-approach in the interpretation of dynamical processes taking place in
interacting systems.Comment: 7 pages, 8 figure
Effective temperatures of a heated Brownian particle
We investigate various possible definitions of an effective temperature for a
particularly simple nonequilibrium stationary system, namely a heated Brownian
particle suspended in a fluid. The effective temperature based on the
fluctuation dissipation ratio depends on the time scale under consideration, so
that a simple Langevin description of the heated particle is impossible. The
short and long time limits of this effective temperature are shown to be
consistent with the temperatures estimated from the kinetic energy and Einstein
relation, respectively. The fluctuation theorem provides still another
definition of the temperature, which is shown to coincide with the short time
value of the fluctuation dissipation ratio
Topological Signature of First Order Phase Transitions
We show that the presence and the location of first order phase transitions
in a thermodynamic system can be deduced by the study of the topology of the
potential energy function, V(q), without introducing any thermodynamic measure.
In particular, we present the thermodynamics of an analytically solvable
mean-field model with a k-body interaction which -depending on the value of k-
displays no transition (k=1), second order (k=2) or first order (k>2) phase
transition. This rich behavior is quantitatively retrieved by the investigation
of a topological invariant, the Euler characteristic, of some submanifolds of
the configuration space. Finally, we conjecture a direct link between the Euler
characteristic and the thermodynamic entropy.Comment: 6 pages, 2 figure
AKLT Models with Quantum Spin Glass Ground States
We study AKLT models on locally tree-like lattices of fixed connectivity and
find that they exhibit a variety of ground states depending upon the spin,
coordination and global (graph) topology. We find a) quantum paramagnetic or
valence bond solid ground states, b) critical and ordered N\'eel states on
bipartite infinite Cayley trees and c) critical and ordered quantum vector spin
glass states on random graphs of fixed connectivity. We argue, in consonance
with a previous analysis, that all phases are characterized by gaps to local
excitations. The spin glass states we report arise from random long ranged
loops which frustrate N\'eel ordering despite the lack of randomness in the
coupling strengths.Comment: 10 pages, 1 figur
Can the jamming transition be described using equilibrium statistical mechanics?
When materials such as foams or emulsions are compressed, they display solid
behaviour above the so-called `jamming' transition. Because compression is done
out-of-equilibrium in the absence of thermal fluctuations, jamming appears as a
new kind of a nonequilibrium phase transition. In this proceeding paper, we
suggest that tools from equilibrium statistical mechanics can in fact be used
to describe many specific features of the jamming transition. Our strategy is
to introduce thermal fluctuations and use statistical mechanics to describe the
complex phase behaviour of systems of soft repulsive particles, before sending
temperature to zero at the end of the calculation. We show that currently
available implementations of standard tools such as integral equations,
mode-coupling theory, or replica calculations all break down at low temperature
and large density, but we suggest that new analytical schemes can be developed
to provide a fully microscopic, quantitative description of the jamming
transition.Comment: 8 pages, 6 figs. Talk presented at Statphys24 (July 2010, Cairns,
Australia
Time-dependent Nonlinear Optical Susceptibility of an Out-of-Equilibrium Soft Material
We investigate the time-dependent nonlinear optical absorption of a clay
dispersion (Laponite) in organic dye (Rhodamine B) water solution displaying
liquid-arrested state transition. Specifically, we determine the characteristic
time of the nonlinear susceptibility build-up due as to the Soret
effect. By comparing with the relaxation time provided by standard
dynamic light scattering measurements we report on the decoupling of the two
collective diffusion times at the two very different length scales during the
aging of the out-of-equilibrium system. With this demonstration experiment we
also show the potentiality of nonlinear optics measurements in the study of the
late stage of arrest in soft materials
On the high density behavior of Hamming codes with fixed minimum distance
We discuss the high density behavior of a system of hard spheres of diameter
d on the hypercubic lattice of dimension n, in the limit n -> oo, d -> oo,
d/n=delta. The problem is relevant for coding theory. We find a solution to the
equations describing the liquid up to very large values of the density, but we
show that this solution gives a negative entropy for the liquid phase when the
density is large enough. We then conjecture that a phase transition towards a
different phase might take place, and we discuss possible scenarios for this
transition. Finally we discuss the relation between our results and known
rigorous bounds on the maximal density of the system.Comment: 15 pages, 6 figure
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