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

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+H_{2}⇔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.

Low-temperature atomistic spin relaxation and non-equilibrium intensive properties using steepest-entropy-ascent quantum-inspired thermodynamics modeling

“…3 and 4 and the remaining figures below is normalized by the relaxation time, τ . This time can be correlated with the real time, t, via comparisons to experimental data [24,25,27] or from ab initio calculations [20,28,32]. Real-time scaling for magnetic relaxation processes has been done in spin The calculated relaxation processes of magnetization from two different initial states prepared using the gamma function, Eq.…”

Multiscale Transient and Steady-State Study of the Influence of Microstructure Degradation and Chromium Oxide Poisoning on Solid Oxide Fuel Cell Cathode Performance

“…The thermodynamic state of the system at any given instant of time is then represented by a probability distribution among the system eigenstates. More detailed descriptions of this novel approach describing the chemical and electrochemical kinetics of reacting quantum systems can be found in [29,30,43]. Given the energy eigenlevels of the system and each nonequilibrium state represented by a probability distribution {p i , i = 1, 2, ⋯}, the SEAQT equation of motion is used to model the chemical and electrochemical reaction pathways.…”

“…To address these issues of time and length scales and the influence of microscopic and mesoscopic parameters, a novel approach based on the SEAQT mathematical framework of intrinsic quantum thermodynamics (IQT) [24][25][26][27][28][29][30][31][32][33][34][35][36] is used here. The resulting model with a significantly smaller computational burden than that of the conventional approach links atomistic-level information with macroscopic, predicting both transport coefficients and reaction rate constants in the presence of coupled and uncoupled phenomena and doing so without the inclusion of all the intermediate models used in the more conventional approach.…”

Ab initiorelaxation times and time-dependent Hamiltonians within the steepest-entropy-ascent quantum thermodynamic framework

“…In such an approach, the evolution of state can occur non-unitarily consistent with both the postulates of QM and thermodynamics. One such approach is that of intrinsic quantum thermodynamics (IQT) [31][32][33][34][35][36][37][38][39][40] and its mathematical framework steepest-entropy-ascent quantum thermodynamics (SEAQT) [41][42][43][44][45][46][47][48][49][50][51][52][53][54][55]. It is this approach and the ones described above that are representative of the contrasting views of the origins of irreversible changes that form the basis of the field of quantum thermodynamics [25,56,57], which has developed over the last four decades and has grown exponentially in the last decade and a half.…”

“…Both reactive and non-reactive quantum and classical systems have been investigated successfully using SEAQT [46][47][48][49][50][51][52][53][54][55] and some validations with experiment have been made [49,50]. It has furthermore been shown that not only does the equation of motion of SEAQT predict the unique thermodynamic path, which the system takes, [37,38] but that the kinetics of this path (i.e., movement along it) and its dynamics (i.e., the time it takes for this movement) can be treated separately [47].…”