The kinetic exclusion process: a tale of two fields

Abstract

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 of 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. Both transport coefficients are coupled via a fluctuation-dissipation theorem, suggesting that the noise terms affecting the local currents have Gaussian properties. We further prove the positivity of entropy production in terms of the microscopic dynamics. 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.