  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. 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.
