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Steepest-entropy-ascent nonequilibrium quantum thermodynamic framework to model chemical reaction rates at an atomistic level

G. P. Beretta1,*, Omar Al-Abbasi2,†, and M. R. von Spakovsky2,‡

  • 1Mechanical and Industrial Engineering Department, Università di Brescia, via Branze 38, 25123 Brescia, Italy
  • 2Center for Energy Systems Research, Mechanical Engineering Department, Virginia Tech, Blacksburg, Virginia 24061, USA

  • *gianpaolo.beretta@unibs.it
  • †omabbasi@vt.edu
  • ‡vonspako@vt.edu
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Phys. Rev. E 95, 042139 – Published 24 April, 2017

DOI: https://doi.org/10.1103/PhysRevE.95.042139

Abstract

The steepest entropy ascent (SEA) dynamical principle provides a general framework for modeling the dynamics of nonequilibrium (NE) phenomena at any level of description, including the atomistic one. It has recently been shown to provide a precise implementation and meaning to the maximum entropy production principle and to encompass many well-established theories of nonequilibrium thermodynamics into a single unifying geometrical framework. Its original formulation in the framework of quantum thermodynamics (QT) assumes the simplest and most natural Fisher-Rao metric to geometrize from a dynamical standpoint the manifold of density operators, which represent the thermodynamic NE states of the system. This simplest SEAQT formulation is used here to develop a general mathematical framework for modeling the NE time evolution of the quantum state of a chemically reactive mixture at an atomistic level. The method is illustrated for a simple two-reaction kinetic scheme of the overall reaction F+H2⇔HF+F in an isolated tank of fixed volume. However, the general formalism is developed for a reactive system subject to multiple reaction mechanisms. To explicitly implement the SEAQT nonlinear law of evolution for the density operator, both the energy and the particle number eigenvalue problems are set up and solved analytically under the dilute gas approximation. The system-level energy and particle number eigenvalues and eigenstates are used in the SEAQT equation of motion to determine the time evolution of the density operator, thus effectively describing the overall kinetics of the reacting system as it relaxes toward stable chemical equilibrium. The predicted time evolution in the near-equilibrium limit is compared to the reaction rates given by a standard detailed kinetic model so as to extract the single time constant needed by the present SEA model.

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Phys. Rev. E 95, 042139– Published 24 April, 2017
  • Received 11 April 2016
  • Revised 13 March 2017

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