Gradient corrections to the local-equilibrium energy-momentum tensor in the Zubarev approach

We compute the expectation value of the energy-momentum tensor of a real scalar field in an approximation which accounts for spacetime gradients of the hydrodynamical variables in local thermodynamical equilibrium. We show that the energy-momentum tensor receives corrections with respect to the standard local-equilibrium result. Notably, the relation between the energy density and pressure, i.e., the equation of state, is modified with respect to the one in global equilibrium. The obtained corrections might be relevant for systems created in relativistic hadron and heavy-ion collisions.