Probing local equilibrium in nonequilibrium fluids

Pozo, J. J. del; Garrido, Pedro L.; Hurtado, Pablo I.

doi:10.1103/physreve.92.022117

Cited by 8 publications

(23 citation statements)

References 91 publications

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“…However, the measured local density and temperature in each case are tightly coupled by the equilibrium EoS, P = ρ(x)T (x), with P the finite-size pressure measured in each simulation, see Fig. S2 and Section II.A in the Supplementary information, validating hypothesis (ii) above and confirming the robustness of MLE far from equilibrium [58]. Note that the thermal walls act as defects (akin to fixed, infinite-mass particles) which disrupt the structure of the surrounding fluid, defining two boundary layers where finite-size corrections mount up.…”

Section: Resultssupporting

confidence: 72%

“…Moreover, similar results hold for all mass ratios µ studied in this paper. In this way, the observed high-precision data collapses confirm the robustness of the MLE property far from equilibrium [1], even in the presence of important finite size effects, validating in an independent manner one of the hypotheses underlying the scaling picture of Section I. We next focus on the nonequilibrium fluid's pressure P and the heat current J flowing through the system, that we measure both in the bulk and at the thermal walls.…”

Section: Macroscopic Local Equilibrium Pressure and Reduced Currentsupporting

confidence: 64%

“…Our first goal is to test the macroscopic local equilibrium (MLE) property directly from our data. As described above, MLE conjectures that local thermodynamic equilibrium holds at the macroscopic level, in the sense that the stationary density and temperature fields are locally related by the equilibrium equation of state (EoS) [1], which for this model is simply the ideal gas EoS,…”

Section: Macroscopic Local Equilibrium Pressure and Reduced Currentmentioning

confidence: 99%

“…(ii) Macroscopic local equilibrium (MLE): This amounts to assume that local thermodynamic equilibrium holds at the macroscopic level, in the sense that the local density and temperature are related by the equilibrium equation of state (EoS) [1]. For the 1d diatomic hard-point gas studied in this paper, it is simply the ideal gas EoS and average the resulting distances.…”

Section: Acknowledgmentsmentioning

confidence: 99%

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A violation of universality in anomalous Fourier’s law

Hurtado

Garrido

2016

Sci Rep

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Since the discovery of long-time tails, it has been clear that Fourier’s law in low dimensions is typically anomalous, with a size-dependent heat conductivity, though the nature of the anomaly remains puzzling. The conventional wisdom, supported by renormalization-group arguments and mode-coupling approximations within fluctuating hydrodynamics, is that the anomaly is universal in 1d momentum-conserving systems and belongs in the Lévy/Kardar-Parisi-Zhang universality class. Here we challenge this picture by using a novel scaling method to show unambiguously that universality breaks down in the paradigmatic 1d diatomic hard-point fluid. Hydrodynamic profiles for a broad set of gradients, densities and sizes all collapse onto an universal master curve, showing that (anomalous) Fourier’s law holds even deep into the nonlinear regime. This allows to solve the macroscopic transport problem for this model, a solution which compares flawlessly with data and, interestingly, implies the existence of a bound on the heat current in terms of pressure. These results question the renormalization-group and mode-coupling universality predictions for anomalous Fourier’s law in 1d, offering a new perspective on transport in low dimensions.

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Section: Resultssupporting

confidence: 72%

Section: Macroscopic Local Equilibrium Pressure and Reduced Currentsupporting

confidence: 64%

Section: Macroscopic Local Equilibrium Pressure and Reduced Currentmentioning

confidence: 99%

Section: Acknowledgmentsmentioning

confidence: 99%

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A violation of universality in anomalous Fourier’s law

Hurtado

Garrido

2016

Sci Rep

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“…However, they do not solve the problem of establishing theoretical interrelations between different macroscopic quantities. In recent works by del Pozo et al [47,48] computer simulation data for the twodimensional hard disks in the heat-conduction steady states are analyzed in terms of the equilibrium-like equation of state and the local Fourier law. Bulk behaviour of the temperature and particle density profiles are shown to obey specific scaling relations valid even for strong nonequilibrium conditions.…”

Section: Introductionmentioning

confidence: 99%

Pressure and entropy of hard spheres in the weakly nonequilibrium heat-conduction steady state

Humenyuk¹

2016

Condens. Matter Phys.

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Thermodynamic quantities of the hard-sphere system in the steady state with a small heat flux are calculated within the continuous media approach. Analytical expressions for pressure, internal energy, and entropy are found in the approximation of the fourth order in temperature gradients. It is shown that the gradient contributions to the internal energy depend on the volume, while the entropy satisfies the second law of thermodynamics for nonequilibrium processes. The calculations are performed for dimensions 3D, 2D, and 1D.

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Simulations of Transport in Hard Particle Systems

Hurtado

Garrido

2020

J Stat Phys

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Hard particle systems are among the most successful, inspiring and prolific models of physics. They contain the essential ingredients to understand a large class of complex phenomena, from phase transitions to glassy dynamics, jamming, or the physics of liquid crystals and granular materials, to mention just a few. As we discuss in this paper, their study also provides crucial insights on the problem of transport out of equilibrium. A main tool in this endeavour are computer simulations of hard particles. Here we review some of our work in this direction, focusing on the hard disks fluid as a model system. In this quest we will address, using extensive numerical simulations, some of the key open problems in the physics of transport, ranging from local equilibrium and Fourier's law to the transition to convective flow in the presence of gravity, the efficiency of boundary dissipation, or the universality of anomalous transport in low dimensions. In particular, we probe numerically the macroscopic local equilibrium hypothesis, which allows to measure the fluid's equation of state in nonequilibrium simulations, uncovering along the way subtle nonlocal corrections to local equilibrium and a remarkable bulk-boundary decoupling phenomenon in fluids out of equilibrium. We further show that the the hydrodynamic profiles that a system develops when driven out of equilibrium by an arbitrary temperature gradient obey universal scaling laws, a result that allows the determination of transport coefficients with unprecedented precission and proves that Fourier's law remains valid in highly nonlinear regimes. Switching on a gravity field against the temperature gradient, we investigate numerically the transition to convective flow. We uncover a surprising two-step transition scenario with two different critical thresholds for the hot bath temperature, a first one where convection kicks but gravity hinders heat transport, and a second critical temperature where a percolation transition of streamlines connecting the hot and cold baths triggers efficient convective heat transport. We also address numerically the efficiency of boundary heat baths to dissipate the energy provided by a bulk driving mechanism. As a bonus track, we depart from the hard disks model to study anomalous transport in a related hard-particle system, the 1d diatomic hard-point gas. We show unambiguously that the universality conjectured for anomalous transport in 1d breaks down for this model, calling into question recent theoretical predictions and offering a new perspective on anomalous transport in low dimensions. Our results show how carefully-crafted numerical simulations Dedicated to Joel L. Lebowitz to celebrate his key role as leading editor of the Journal of Statistical Physics.

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Probing local equilibrium in nonequilibrium fluids

Cited by 8 publications

References 91 publications

A violation of universality in anomalous Fourier’s law

A violation of universality in anomalous Fourier’s law

Pressure and entropy of hard spheres in the weakly nonequilibrium heat-conduction steady state

Simulations of Transport in Hard Particle Systems

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