The assumption of local equilibrium is validated in four different systems where heat and mass are transported. Mass fluxes up to 13kmol=m2 s and temperature gradients up to 1012 K=m were used. A two-component mixture, two vapor–liquid interfaces, a chemical reaction in a temperature gradient and gas adsorbed in zeolite were studied using non-equilibrium molecular dynamics simulations. In all cases, we verified that thermodynamic variables obeyed normal thermodynamic relations, with an accuracy better than 5%. The heat and mass fluxes, and the reaction rate were linearly related to the driving forces. Onsager's reciprocal relations were validated for two systems. Equipartition of kinetic energy applied to all directions. There was no need to invoke any dependence of the thermodynamic variables on the gradients. Away from global equilibrium, the local velocity distribution was found to deviate from the Maxwell distribution in the direction of transport. The deviation was in a form that is used by the Enskog method to solve the Boltzmann equation. New general criteria were formulated for thermodynamic state variables, P. In order to obey local equilibrium, the relative fluctuation in the state variable needs only to fulfill dP=Pt1= ffiffiffiffi N p , where N is the number of particles in the volume element. The variation of the variable in the direction of transport needs to fulfill DP=P ¼ ‘xrP=P51, where the length of the volume element in direction of transport, ‘x, is of the order of the diameter of a molecule. These criteria are much less restrictive than proposed earlier, and allows us to use thermodynamic equations in open volume elements with a surprisingly small number (8–18) of particles.