The kinetic exclusion process: a tale of two fields

Gutiérrez-Ariza, Carlos; Hurtado, Pablo I.

doi:10.1088/1742-5468/ab4587

Cited by 14 publications

(6 citation statements)

References 138 publications

(210 reference statements)

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“…in hard disks, using two new powerful tools that have appeared in recent years, namely macroscopic fluctuation theory (MFT) [5] and advanced simulation techniques for rare (large-deviation) events [63,[162][163][164][165]. Note that the MFT approach needs a general, nonlinear formulation of fluctuating hydrodynamics for systems with several conservation laws, as recently obtained for stochastic lattice gases [166].…”

Section: Discussion and Outlookmentioning

confidence: 99%

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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Section: Discussion and Outlookmentioning

confidence: 99%

Simulations of Transport in Hard Particle Systems

Hurtado

Garrido

2020

J Stat Phys

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“…The classic KMP model [KMP82] and BEP models [PRV14] are specifically for crystals. The recent kinetic exclusion process [GAH19] seems more suitable for solutes, but a detailed knowledge of the fluctuations is still unknown.…”

Section: Microscopic Modelmentioning

confidence: 99%

Anisothermal chemical reactions: Onsager–Machlup and macroscopic fluctuation theory

Renger¹

2022

J. Phys. A: Math. Theor.

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We study a micro and macroscopic model for chemical reactions with feedback between reactions and temperature of the solute. The first result concerns the quasipotential as the large-deviation rate of the microscopic invariant measure. The second result is an application of modern Onsager–Machlup theory to the pathwise large deviations, in case the system is in detailed balance. The third result is an application of macroscopic fluctuation theory to the reaction flux large deviations, in case the system is in complex balance.

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“…At each (exponentially distributed) random move the total energy of a randomly chosen pair of nearest neighbors is redistributed among them randomly according to uniform distribution, and the process continues. Because of its simplicity the KMP model has become a paradigmatic model in the studies of fluctuations, including large deviations, of heat transfer in classical macroscopic nonequilibrium systems [4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19].…”

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confidence: 99%

Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model

Bettelheim¹,

Smith²,

Meerson³

2022

Preprint

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We investigate non-stationary heat transfer in the Kipnis-Marchioro-Presutti (KMP) lattice gas model at long times in one dimension when starting from a localized heat distribution. At large scales this initial condition can be described as a delta-function, u(x, t = 0) = W δ(x). We characterize the process by the heat, transferred to the right of a specified point x = X by time T ,and study the full probability distribution P(J, X, T ). The particular case of X = 0 has been recently solved [Bettelheim et al. Phys. Rev. Lett. 128, 130602 (2022)]. At fixed J, the distribution P as a function of X and T has the same long-time dynamical scaling properties as the position of a tracer in a single-file diffusion. Here we evaluate P(J, X, T ) by exploiting the recently uncovered complete integrability of the equations of the macroscopic fluctuation theory (MFT) for the KMP model and using the Zakharov-Shabat inverse scattering method. We also discuss asymptotics of P(J, X, T ) which we extract from the exact solution, and also obtain perturbatively directly from the MFT equations.

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The kinetic exclusion process: a tale of two fields

Cited by 14 publications

References 138 publications

Simulations of Transport in Hard Particle Systems

Simulations of Transport in Hard Particle Systems

Anisothermal chemical reactions: Onsager–Machlup and macroscopic fluctuation theory

Full Statistics of Nonstationary Heat Transfer in the Kipnis-Marchioro-Presutti Model

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