Steepest-entropy-ascent quantum thermodynamic framework for describing the non-equilibrium behavior of a chemically reactive system at an atomistic level

Steepest-Entropy-Ascent Quantum Thermodynamics (SEAQT) provides a general framework for the description of non-equilibrium phenomena at any level, particularly the atomistic one. This theory and its dynamical postulate are used here to develop a general mathematical framework, which at an atomistic level, in particular, can be used to predict the non-equilibrium evolution in state of a closed, chemically reactive mixture such as the one examined here, i.e., a mixture of hydrogen (H2) and flourine (F) contained in an isolated tank of fixed volume. The general framework provided, however, is written for a reactive system subject to multiple reaction mechanisms. To predict this evolution in state, both the energy and particle number eigenvalue problems for a dilute gas are set up and solved analytically. Wall and non-ideal-gas behavior effects are neglected, although the extension to dense gases is straightforward but left for a future paper. The system-level energy and particle number eigenvalues and eigenstates found are used in the nonlinear equation of motion of SEAQT to determine the time evolution of the thermodynamic state of the system, thus, effectively describing the reaction kinetics of the reaction and the system's relaxation to stable equilibrium. The predicted time evolution is then compared to the results of a standard detailed kinetic model used, in the near-equilibrium limit, to extract the single time constant needed by the SEAQT equation of motion.