Predicting Coupled Electron and Phonon Transport Using Steepest-Entropy-Ascent Quantum Thermodynamics

The current state of the art for determining thermoelectric properties is limited to the investigation of electrons or phonons without including the inherent electron-phonon coupling that is in all materials. This gives rise to limitations in accurately calculating base material properties that are in good agreement with experimental data. Steepest-entropy-ascent quantum thermodynamics is a general non-equilibrium thermodynamic ensemble framework that provides a general equation of motion for non-equilibrium system state evolution. This framework utilizes the electron and phonon density of states as input to compute material properties, while taking into account the electron-phonon coupling. It is able to span across multiple spatial and temporal scales in a single analysis. Any system's thermoelectric properties can, therefore, be attained provided the accurately determined density of states is available.Comment: Supplementary Materials Section is the last two pages of the manuscrip

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

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 towards 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