17 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
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
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
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
Topological properties of the mean field phi^4 model
We study the thermodynamics and the properties of the stationary points
(saddles and minima) of the potential energy for a phi^4 mean field model. We
compare the critical energy Vc (i.e. the potential energy V(T) evaluated at the
phase transition temperature Tc) with the energy V{theta} at which the saddle
energy distribution show a discontinuity in its derivative. We find that, in
this model, Vc >> V{theta}, at variance to what has been found in the
literature for different mean field and short ranged systems. By direct
calculation of the energy Vs(T) of the ``inherent saddles'', i.e. the saddles
visited by the equilibrated system at temperature T, we find that Vs(Tc) ~
V{theta}. Thus, we argue that the thermodynamic phase transition is related to
a change in the properties of the inherent saddles rather then to a change of
the topology of the potential energy surface at T=Tc. Finally, we discuss the
approximation involved in our analysis and the generality of our method.Comment: 14 pages, 9 figure
Crossover between Equilibrium and Shear-controlled Dynamics in Sheared Liquids
We present a numerical simulation study of a simple monatomic Lennard-Jones
liquid under shear flow, as a function of both temperature and shear rate. By
investigating different observables we find that i) It exists a line in the
(temperature-shear) plane that sharply marks the boarder between an
``equilibrium'' and a ``shear-controlled'' region for both the dynamic and the
thermodynamic quantities; and ii) Along this line the structural relaxation
time, is proportional to the inverse shear rate, i.e. to the typical time-scale
introduced by the shear flow. Above the line the liquid dynamics is unaffected
by the shear flow, while below it both temperature and shear rate control the
particle motion.Comment: 14 pages, 5 figure
Glassy behavior of light
We study the nonlinear dynamics of a multi-mode random laser using the
methods of statistical physics of disordered systems. A replica-symmetry
breaking phase transition is predicted as a function of the pump intensity. We
thus show that light propagating in a random non-linear medium displays glassy
behavior, i.e. the photon gas has a multitude of metastable states and a non
vanishing complexity, corresponding to mode-locking processes in random lasers.
The present work reveals the existence of new physical phenomena, and
demonstrates how nonlinear optics and random lasers can be a benchmark for the
modern theory of complex systems and glasses.Comment: 5 pages, 1 figur
Dynamics and geometric properties of the k-Trigonometric model
We analyze the dynamics and the geometric properties of the Potential Energy
Surfaces (PES) of the k-Trigonometric Model (kTM), defined by a fully-connected
k-body interaction. This model has no thermodynamic transition for k=1, a
second order one for k=2, and a first order one for k>2. In this paper we i)
show that the single particle dynamics can be traced back to an effective
dynamical system (with only one degree of freedom); ii) compute the diffusion
constant analytically; iii) determine analytically several properties of the
self correlation functions apart from the relaxation times which we calculate
numerically; iv) relate the collective correlation functions to the ones of the
effective degree of freedom using an exact Dyson-like equation; v) using two
analytical methods, calculate the saddles of the PES that are visited by the
system evolving at fixed temperature. On the one hand we minimize |grad V|^2,
as usually done in the numerical study of supercooled liquids and, on the other
hand, we compute the saddles with minimum distance (in configuration space)
from initial equilibrium configurations. We find the same result from the two
calculations and we speculate that the coincidence might go beyond the specific
model investigated here.Comment: 36 pages, 13 figure
Glassy behavior of light in random lasers
A theoretical analysis [Angelani et al., Phys. Rev. Lett. 96, 065702 (2006)]
predicts glassy behaviour of light in a nonlinear random medium. This implies
slow dynamics related to the presence of many metastable states. We consider
very general equations (that also apply to other systems, like Bose-Condensed
gases) describing light in a disordered non-linear medium and through some
approximations we relate them to a mean-field spin-glass-like model. The model
is solved by the replica method, and replica-symmetry breaking phase transition
is predicted. The transition describes a mode-locking process in which the
phases of the modes are locked to random (history and sample-dependent) values.
The results are based on very general theory, and embrace a variety of physical
phenomena.Comment: 21 pages, 3 figures. Revised and enlarged version. To be published in
Physical Review
Work and heat fluctuations in two-state systems: a trajectory thermodynamics formalism
Two-state models provide phenomenological descriptions of many different
systems, ranging from physics to chemistry and biology. We investigate work
fluctuations in an ensemble of two-state systems driven out of equilibrium
under the action of an external perturbation. We calculate the probability
density P(W) that a work equal to W is exerted upon the system along a given
non-equilibrium trajectory and introduce a trajectory thermodynamics formalism
to quantify work fluctuations in the large-size limit. We then define a
trajectory entropy S(W) that counts the number of non-equilibrium trajectories
P(W)=exp(S(W)/kT) with work equal to W. A trajectory free-energy F(W) can also
be defined, which has a minimum at a value of the work that has to be
efficiently sampled to quantitatively test the Jarzynski equality. Within this
formalism a Lagrange multiplier is also introduced, the inverse of which plays
the role of a trajectory temperature. Our solution for P(W) exactly satisfies
the fluctuation theorem by Crooks and allows us to investigate
heat-fluctuations for a protocol that is invariant under time reversal. The
heat distribution is then characterized by a Gaussian component (describing
small and frequent heat exchange events) and exponential tails (describing the
statistics of large deviations and rare events). For the latter, the width of
the exponential tails is related to the aforementioned trajectory temperature.
Finite-size effects to the large-N theory and the recovery of work
distributions for finite N are also discussed. Finally, we pay particular
attention to the case of magnetic nanoparticle systems under the action of a
magnetic field H where work and heat fluctuations are predicted to be
observable in ramping experiments in micro-SQUIDs.Comment: 28 pages, 14 figures (Latex