Steepest-entropy-ascent model of mesoscopic quantum systems far from equilibrium along with generalized thermodynamic definitions of measurement and reservoir

Abstract

This paper presents a nonequilibrium, first-principles, thermodynamic-ensemble based model for the relaxation process of interacting non-equilibrium systems. This model is formulated using steepest-entropy-ascent quantum thermodynamics (SEAQT) and its equation of motion for a grand canonical ensemble and is applied to a many particle system of classical or indistinguishable particles. Two kinds of interactions are discussed, including pure heat diffusion and heat and mass diffusion together. Since no local equilibrium assumption is made, the conjugate fluxes and forces are intrinsic to the subspaces of the state space of one system and/or of the state space of two interacting systems. They are derived via the concepts of hypoequilibrium state and nonequilibrium intensive properties, which describe the nonmutual equilibrium status between subspaces of the thermodynamic state space of a single system and/or of the state space of two interacting systems. The Onsager relations are shown to be thermodynamic kinematic features of the system and are found without knowledge of the detailed mechanics of the dynamic process. A fundamental thermodynamic explanation for the measurement of each intensive property of a system in a nonequilibrium state is given. The fundamental thermodynamic definition of reservoir is also discussed. In addition, the equation of motion for a system undergoing multiple interactions is provided, which permits the modeling of a network of local systems in nonequilibrium at any spatial and temporal scale. Finally, the physical features of a nonequilibrium measurement is illustrated via a case study, and the general validity of the equal probability condition is discussed.

CH4 Adsorption Probability on GaN(0001) and (000−1) during Metalorganic Vapor Phase Epitaxy and Its Relationship to Carbon Contamination in the Films

“…SEAQT is a thermodynamic-ensemble-based, non-phenomenological framework that can predict the behavior of non-equilibrium processes, even those far from equilibrium. This framework has been developed and applied to both non-reacting and reacting systems at multiple spatial and temporal scales and validated via comparisons with experiments [26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47]. In 2016, Li and von Spakovsky developed a density of states method and introduced the concept of a hypoequilibrium state, which extends the computational applicability of this framework across all spatial and temporal scales [41].…”

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

“…In addition, a SEAQT equation of motion for a system interacting with a reservoir can be derived by taking one of the subsystems in the composite system as a reservoir. This strategy has been developed by Li and von Spakovsky for heat and mass interactions [21][22][23]; the methodology is applied here to formulate an equation of motion for subsystems undergoing heat and magnetic field interactions.…”

“…Here, the concept is briefly described and nonequilibrium temperature and magnetic field strength are defined (details are found in Refs. [21][22][23]).…”

“…Furthermore, as proven in Refs. [21,23], once in a M th -order hypoequilibrium state, the system remains in such a state throughout the entire kinetic evolution process predicted by the SEAQT equation of motion, and the relaxation paths can be simply described by the time dependence of the intensive properties in each subspace. This means that the time evolution of the probability distribution in subspace (or subsystem) M can be described by…”

“…(9) The time evolution of the intensive properties are determined from the equation of motion for the intensive properties [23] given by…”