Category Archives: local thermodynamic equilibrium

The kinetic exclusion process: A tale of two fields

C. Gutiérrez-Ariza, P. I. Hurtado

We introduce a general class of stochastic lattice gas models, and derive their fluctuating hydrodynamics description in the large size limit under a local equilibrium hypothesis. The model consists in energetic particles on a lattice subject to exclusion interactions, which move and collide stochastically with energy-dependent rates. The resulting fluctuating hydrodynamics equations exhibit nonlinear coupled particle and energy transport, including particle currents due to temperature gradients (Soret effect) and energy flow due to concentration gradients (Dufour effect). The microscopic dynamical complexity is condensed in just two matrices of transport coefficients: the diffusivity matrix (or equivalently the Onsager matrix) generalizing Fick-Fourier’s law, and the mobility matrix controlling current fluctuations, which are coupled via a fluctuation-dissipation theorem. Interestingly, the positivity of entropy production in the system then leads to detailed constraints on the microscopic dynamics. We further demonstrate the Gaussian character of the noise terms affecting the local currents. The so-called kinetic exclusion process has as limiting cases two of the most paradigmatic models of nonequilibrium physics, namely the symmetric simple exclusion process of particle diffusion and the Kipnis-Marchioro-Presutti model of heat flow, making it the ideal testbed where to further develop modern theories of nonequilibrium behavior.

J. Stat. Mech. (2019) 103203; arXiv:1905.03142

Probing local equilibrium in nonequilibrium fluids

J.J. del Pozo, P.L. Garrido, P.I. Hurtado

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.

Phys. Rev. E 92, 022117 (2015)arXiv:1407.3113

Scaling laws and bulk-boundary decoupling in heat flow

J.J. del Pozo, P.L. Garrido, P.I. Hurtado

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.

Additional material: video demonstrating the scaling procedure (credit: J. del Pozo 2014)

Phys. Rev. E 91, 032116 (2015)arXiv:1401.5244