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P. L. Garrido

Publications and source records attributed to P. L. Garrido.

At least 19 recordsLinked to original sources
arXiv2025

Scaling laws for stationary Navier-Stokes-Fourier flows and the unreasonable effectiveness of hydrodynamics at the molecular level

Hydrodynamics provides a universal description of the emergent collective dynamics of vastly different many-body systems, based solely on their symmetries and conservation laws. Here we harness this universality, encoded in the Navier-Stokes-Fourier (NSF) equations, to find general scaling laws for the stationary uniaxial solutions of the compressible NSF problem far from equilibrium. We show for general transport coefficients that the steady density and temperature fields are functions of the pressure and a kinetic field that quantifies the quadratic excess velocity relative to the ratio of heat flux and shear stress. This kinetic field obeys in turn a spatial scaling law controlled by pressure and stress, which is inherited by the stationary density and temperature fields. We develop a scaling approach to measure the associated master curves, and confirm our predictions through compelling data collapses in large-scale molecular dynamics simulations of paradigmatic model fluids. Interestingly, the robustness of the scaling laws in the face of significant finite-size effects reveals the surprising accuracy of NSF equations in describing molecular-scale stationary flows. Overall, these scaling laws provide a novel characterization of stationary states in driven fluids.

cond-mat.stat-mech↗
arXiv2024

Time evolution of the Boltzmann entropy for a nonequilibrium dilute gas

We investigate the time evolution of the Boltzmann entropy of a dilute gas of N particles, N>>1, as it undergoes a free expansion doubling its volume. The microstate of the system, a point in the 4N dimensional phase space, changes in time via Hamiltonian dynamics. Its entropy, at any time $t$, is given by the logarithm of the phase space volume of all the microstates giving rise to its macrostate at time $t$. The macrostates that we consider are defined by coarse graining the one-particle phase space into cells $Δ_α$. The initial and final macrostates of the system are equilibrium states in volumes $V$ and $2V$, with the same energy $E$ and particle number $N$. Their entropy per particle is given, for sufficiently large systems, by the thermodynamic entropy as a function of the particle and energy density, whose leading term is independent of the size of the $Δ_α$. The intermediate (non-equilibrium) entropy does however depend on the size of the cells $Δ_α$. Its change with time is due to (i) dispersal in physical space from free motion and to (ii) the collisions between particles which change their velocities. The former depends strongly on the size of the velocity coarse graining $Δv$: it produces entropy at a rate proportional to $Δv$. This dependence is investigated numerically and analytically for a dilute two-dimensional gas of hard discs. It becomes significant when the mean free path between collisions is of the same order or larger than the length scale of the initial spatial inhomogeneity. In the opposite limit, the rate of entropy production is essentially independent of $Δv$ and is given by the Boltzmann equation for the limit $Δv\rightarrow 0$. We show that when both processes are active the time dependence of the entropy has a scaling form involving the ratio of the rates of its production by the two processes.

cond-mat.stat-mech↗
arXiv2022

Molecular hints of two-step transition to convective flow via streamline percolation

Convection is a key transport phenomenon important in many different areas, from hydrodynamics and ocean circulation to planetary atmospheres or stellar physics. However its microscopic understanding still remains challenging. Here we numerically investigate the onset of convective flow in a compressible (non-Oberbeck-Boussinesq) hard disk fluid under a temperature gradient in a gravitational field. We uncover a surprising two-step transition scenario with two different critical temperatures. When the bottom plate temperature reaches a first threshold, convection kicks in (as shown by a structured velocity field) but gravity results in hindered heat transport as compared to the gravity-free case. It is at a second (higher) temperature that a percolation transition of advection zones connecting the hot and cold plates triggers efficient convective heat transport. Interestingly, this novel picture for the convection instability opens the door to unknown piecewise-continuous solutions to the Navier-Stokes equations.

cond-mat.stat-mech↗
arXiv2019

Infinite family of universal profiles for heat current statistics in Fourier's law

Using tools from large deviation theory, we study fluctuations of the heat current in a model of $d$-dimensional incompressible fluid driven out of equilibrium by a temperature gradient. We find that the most probable temperature fields sustaining atypical values of the global current can be naturally classified in an infinite set of curves, allowing us to exhaustively analyze their topological properties and to define universal profiles onto which all optimal fields collapse. We also compute the statistics of empirical heat current, where we find remarkable logarithmic tails for large current fluctuations orthogonal to the thermal gradient. Finally, we determine explicitly a number of cumulants of the current distribution, finding remarkable relations between them.

cond-mat.stat-mech↗
arXiv2017

Order and symmetry-breaking in the fluctuations of driven systems

Dynamical phase transitions (DPTs) in the space of trajectories are one of the most intriguing phenomena of nonequilibrium physics, but their nature in realistic high-dimensional systems remains puzzling. Here we observe for the first time a DPT in the current vector statistics of an archetypal two-dimensional (2d) driven diffusive system, and characterize its properties using macroscopic fluctuation theory. The complex interplay among the external field, anisotropy and vector currents in 2d leads to a rich phase diagram, with different symmetry-broken fluctuation phases separated by lines of first- and second-order DPTs. Remarkably, different types of 1d order in the form of jammed density waves emerge to hinder transport for low-current fluctuations, revealing a connection between rare events and self-organized structures which enhance their probability.

cond-mat.stat-mech↗
arXiv2017

Structure of the optimal path to a fluctuation

Macroscopic fluctuations have become an essential tool to understand physics far from equilibrium due to the link between their statistics and nonequilibrium ensembles. The optimal path leading to a fluctuation encodes key information on this problem, shedding light on e.g. the physics behind the enhanced probability of rare events out of equilibrium, the possibility of dynamic phase transitions and new symmetries. This makes the understanding of the properties of these optimal paths a central issue. Here we derive a fundamental relation which strongly constraints the architecture of these optimal paths for general $d$-dimensional nonequilibrium diffusive systems, and implies a non-trivial structure for the dominant current vector fields. Interestingly, this general relation (which encompasses and explains previous results) makes manifest the spatio-temporal non-locality of the current statistics and the associated optimal trajectories.

cond-mat.stat-mech↗
arXiv2015

Probing local equilibrium in nonequilibrium fluids

We use extensive computer simulations to probe local thermodynamic equilibrium (LTE) in a quintessential model fluid, the two-dimensional hard-disks system. We show that macroscopic LTE is a property much stronger than previously anticipated, even in the presence of important finite size effects, revealing a remarkable bulk-boundary decoupling phenomenon in fluids out of equilibrium. This allows us to measure the fluid's equation of state in simulations far from equilibrium, with an excellent accuracy comparable to the best equilibrium simulations. Subtle corrections to LTE are found in the fluctuations of the total energy which strongly point out to the nonlocality of the nonequilibrium potential governing the fluid's macroscopic behavior out of equilibrium.

cond-mat.stat-mech↗
arXiv2015

Scaling laws and bulk-boundary decoupling in heat flow

When driven out of equilibrium by a temperature gradient, fluids respond by developing a nontrivial, inhomogeneous structure according to the governing macroscopic laws. Here we show that such structure obeys strikingly simple scaling laws arbitrarily far from equilibrium, provided that both macroscopic local equilibrium and Fourier's law hold. Extensive simulations of hard disk fluids confirm the scaling laws even under strong temperature gradients, implying that Fourier's law remains valid in this highly nonlinear regime, with putative corrections absorbed into a nonlinear conductivity functional. In addition, our results show that the scaling laws are robust in the presence of strong finite-size effects, hinting at a subtle bulk-boundary decoupling mechanism which enforces the macroscopic laws on the bulk of the finite-sized fluid. This allows to measure for the first time the marginal anomaly of the heat conductivity predicted for hard disks.

cond-mat.stat-mech↗
arXiv2006

Demagnetization via Nucleation of the Nonequilibrium Metastable Phase in a Model of Disorder

We study both analytically and numerically metastability and nucleation in a two-dimensional nonequilibrium Ising ferromagnet. Canonical equilibrium is dynamically impeded by a weak random perturbation which models homogeneous disorder of undetermined source. We present a simple theoretical description, in perfect agreement with Monte Carlo simulations, assuming that the decay of the nonequilibrium metastable state is due, as in equilibrium, to the competition between the surface and the bulk. This suggests one to accept a nonequilibrium "free-energy" at a mesoscopic/cluster level, and it ensues a nonequilibrium "surface tension" with some peculiar low-T behavior. We illustrate the occurrence of intriguing nonequilibrium phenomena, including: (i) Noise-enhanced stabilization of nonequilibrium metastable states; (ii) reentrance of the limit of metastability under strong nonequilibrium conditions; and (iii) resonant propagation of domain walls. The cooperative behavior of our system may also be understood in terms of a Langevin equation with additive and multiplicative noises. We also studied metastability in the case of open boundaries as it may correspond to a magnetic nanoparticle. We then observe burst-like relaxation at low T, triggered by the additional surface randomness, with scale-free avalanches which closely resemble the type of relaxation reported for many complex systems. We show that this results from the superposition of many demagnetization events, each with a well- defined scale which is determined by the curvature of the domain wall at which it originates. This is an example of (apparent) scale invariance in a nonequilibrium setting which is not to be associated with any familiar kind of criticality.

cond-mat.stat-mech↗
arXiv2006

Metastability, nucleation, and noise-enhanced stabilization out of equilibrium

We study metastability and nucleation in a kinetic two-dimensional Ising model which is driven out of equilibrium by a small random perturbation of the usual dynamics at temperature T. We show that, at a mesoscopic/cluster level, a nonequilibrium potential describes in a simple way metastable states and their decay. We thus predict noise-enhanced stability of the metastable phase and resonant propagation of domain walls at low T. This follows from the nonlinear interplay between thermal and nonequilibrium fluctuations, which induces reentrant behavior of the surface tension as a function of T. Our results, which are confirmed by Monte Carlo simulations, can be also understood in terms of a Langevin equation with competing additive and multiplicative noises.

cond-mat.stat-mech↗
arXiv2006

Boundary Dissipation in a Driven Hard Disk System

A simulation is performed aiming at checking the existence of a well defined stationary state for a two dimensional system of driven hard disks when energy dissipation takes place at the system boundaries and no bulk impurities are present

cond-mat.stat-mech↗
arXiv2006

Lattice versus Lennard-Jones models with a net particle flow

We present and study lattice and off-lattice microscopic models in which particles interact via a local anisotropic rule. The rule induces preferential hopping along one direction, so that a net current sets in if allowed by boundary conditions. This may be viewed as an oversimplification of the situation concerning certain traffic and flow problems. The emphasis in our study is on the influence of dynamic details on the resulting (non-equilibrium) steady state. In particular, we shall discuss on the similarities and differences between a lattice model and its continuous counterpart, namely, a Lennard-Jones analogue in which the particles' coordinates vary continuously. Our study, which involves a large series of computer simulations, in particular reveals that spatial discretization will often modify the resulting morphological properties and even induce a different phase diagram and criticality.

cond-mat.stat-mech↗
arXiv2006

Algorithms for identification and categorization

The main features of a family of efficient algorithms for recognition and classification of complex patterns are briefly reviewed. They are inspired in the observation that fast synaptic noise is essential for some of the processing of information in the brain.

q-bio.NC↗
arXiv2006

Non-equilibrium Anisotropic Phases, Nucleation and Critical Behavior in a Driven Lennard-Jones Fluid

We describe short-time kinetic and steady-state properties of the non--equilibrium phases, namely, solid, liquid and gas anisotropic phases in a driven Lennard-Jones fluid. This is a computationally-convenient two-dimensional model which exhibits a net current and striped structures at low temperature, thus resembling many situations in nature. We here focus on both critical behavior and details of the nucleation process. In spite of the anisotropy of the late--time spinodal decomposition process, earlier nucleation seems to proceed by Smoluchowski coagulation and Ostwald ripening, which are known to account for nucleation in equilibrium, isotropic lattice systems and actual fluids. On the other hand, a detailed analysis of the system critical behavior rises some intriguing questions on the role of symmetries; this concerns the computer and field-theoretical modeling of non-equilibrium fluids.

cond-mat.soft↗
arXiv2006

Understanding Scale Invariance in a Minimal Model of Complex Relaxation Phenomena

We report on the computer study of a lattice system that relaxes from a metastable state. Under appropriate nonequilibrium randomness, relaxation occurs by avalanches, i.e., the model evolution is discontinuous and displays many scales in a way that closely resembles the relaxation in a large number of complex systems in nature. Such apparent scale invariance simply results in the model from summing over many exponential relaxations, each with a scale which is determined by the curvature of the domain wall at which the avalanche originates. The claim that scale invariance in a nonequilibrium setting is to be associated with criticality is therefore not supported. Some hints that may help in checking this experimentally are discussed.

cond-mat.dis-nn↗
arXiv2005

Lennard--Jones and Lattice Models of Driven Fluids

We introduce a nonequilibrium off--lattice model for anisotropic phenomena in fluids. This is a Lennard--Jones generalization of the driven lattice--gas model in which the particles' spatial coordinates vary continuously. A comparison between the two models allows us to discuss some exceptional, hardly realistic features of the original discrete system --which has been considered a prototype for nonequilibrium anisotropic phase transitions. We thus help to clarify open issues, and discuss on the implications of our observations for future investigation of anisotropic phase transitions.

cond-mat.stat-mech↗
arXiv2005

Switching between memories in neural automata with synaptic noise

We present a stochastic neural automata in which activity fluctuations and synaptic intensities evolve at different temperature, the latter moving through a set of stored patterns. The network thus exhibits various retrieval phases, including one which depicts continuous switching between attractors. The switching may be either random or more complex, depending on the system parameters values.

cond-mat.stat-mech↗