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Steepest-Entropy-Ascent Quantum Thermodynamics (SEAQT) provides a generalframework for the description of non-equilibrium phenomena at any level,particularly the atomistic one. This theory and its dynamical postulate areused here to develop a general mathematical framework, which at an atomisticlevel, in particular, can be used to predict the non-equilibrium evolution instate 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 tankof fixed volume. The general framework provided, however, is written for areactive system subject to multiple reaction mechanisms. To predict thisevolution in state, both the energy and particle number eigenvalue problems fora dilute gas are set up and solved analytically. Wall and non-ideal-gasbehavior effects are neglected, although the extension to dense gases isstraightforward but left for a future paper. The system-level energy andparticle number eigenvalues and eigenstates found are used in the nonlinearequation of motion of SEAQT to determine the time evolution of thethermodynamic state of the system, thus, effectively describing the reactionkinetics of the reaction and the system's relaxation to stable equilibrium. Thepredicted time evolution is then compared to the results of a standard detailedkinetic model used, in the near-equilibrium limit, to extract the single timeconstant needed by the SEAQT equation of motion.

physical review. e

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