Local Equilibrium Approximation in Non-Equilibrium Thermodynamics of Diffusion

Local equilibrium approximation (LEA) is a central assumption in many applications of non-equilibrium thermodynamics involving the transport of energy, mass, and momentum. However, assessing the validity of the LEA remains challenging due to the limited development of tools for characterizing non-equilibrium states compared to equilibrium states. To address this, we have developed a theory based on kinetic theory, which provides a nonlinear extension of the telegrapher's equation commonly discussed in non-equilibrium frameworks that extend beyond LEA. A key result of this theory is a steady-state diffusion equation that accounts for the constraint imposed by available thermal energy on the diffusion flux. The theory is suitable for analysis of steady-state composition profiles and can be used to quantify the deviation from the local equilibrium. To validate the theory and test LEA, we performed molecular dynamics simulations on a two-component system where the two components had identical physical properties. The results show that deviation from the local equilibrium can be systematically quantified, and for the diffusion process we have studied here, we have confirmed that LEA remains accurate even under extreme concentration gradients in gas mixtures.