Quantifying the uncertainty of the renewable energy generation units and loads is critical to ensure the dynamic security of next-generation power systems. To achieve that goal, the time-consuming Monte Carlo simulations are usually used, which is not suitable for online dynamic analysis of large-scale power systems. To circumvent this difficulty, two uncertainty quantification approaches using polynomial-chaos-based methods are proposed and investigated. The first approach is the generalized polynomial chaos method that is able to reduce the computing time by three orders of magnitude compared with Monte Carlo methods while achieving the same accuracy. We find that this approach is very useful for short-term power system dynamic simulations, but it may produce unreliable results for long-term simulations. To address the weakness of that approach, we present the second method, namely the multi-element generalized-polynomial-chaos method. It is shown that this method is more accurate and more numerically stable than the generalized polynomial chaos method. Since the uncertainties of the renewable energy generation units and loads can follow very different distributions, we extend the Stieltjes' recursive procedure that allows us to derive the orthogonal basis functions for any assumed probability distribution of the input random variables. Simulations show the effectiveness of the proposed approaches.

The steepest-entropy-ascent quantum thermodynamic (SEAQT) framework is used to model the decoherence that occurs during the state evolution of two different microscopic composite systems. The test cases are a $\text{two}-\text{spin}-\frac{1}{2}-\text{particle}$ composite system and a particle-photon field composite system like that experimentally studied in cavity quantum electrodynamics. The first system is used to study the characteristics of the nonlinear equation of motion of the SEAQT framework when modeling the state evolution of a microscopic composite system with particular interest in the phenomenon of decoherence. The second system is used to compare the numerical predictions of the SEAQT framework with experimental cavity quantum electrodynamic data available in the literature. For the two different numerical cases presented, the time evolution of the density operator of the composite system as well as that of the reduced operators belonging to the two constituents is traced from an initial nonequilibrium state of the composite along its relaxation towards stable equilibrium. Results show for both cases how the initial entanglement and coherence is dissipated during the state relaxation towards a state of stable equilibrium.

This paper presents a study of the nonequilibrium relaxation process of chemically reactive systems using steepest-entropy-ascent quantum thermodynamics (SEAQT). The trajectory of the chemical reaction, i.e., the accessible intermediate states, is predicted and discussed. The prediction is made using a thermodynamic-ensemble approach, which does not require detailed information about the particle mechanics involved (e.g., the collision of particles). Instead, modeling the kinetics and dynamics of the relaxation process is based on the principle of steepest-entropy ascent (SEA) or maximum-entropy production, which suggests a constrained gradient dynamics in state space. The SEAQT framework is based on general definitions for energy and entropy and at least theoretically enables the prediction of the nonequilibrium relaxation of system state at all temporal and spatial scales. However, to make this not just theoretically but computationally possible, the concept of density of states is introduced to simplify the application of the relaxation model, which in effect extends the application of the SEAQT framework even to infinite energy eigenlevel systems. The energy eigenstructure of the reactive system considered here consists of an extremely large number of such levels (on the order of ${10}^{130}$) and yields to the quasicontinuous assumption. The principle of SEA results in a unique trajectory of system thermodynamic state evolution in Hilbert space in the nonequilibrium realm, even far from equilibrium. To describe this trajectory, the concepts of subsystem hypoequilibrium state and temperature are introduced and used to characterize each system-level, nonequilibrium state. This definition of temperature is fundamental rather than phenomenological and is a generalization of the temperature defined at stable equilibrium. In addition, to deal with the large number of energy eigenlevels, the equation of motion is formulated on the basis of the density of states and a set of associated degeneracies. Their significance for the nonequilibrium evolution of system state is discussed. For the application presented, the numerical method used is described and is based on the density of states, which is specifically developed to solve the SEAQT equation of motion. Results for different kinds of initial nonequilibrium conditions, i.e., those for gamma and Maxwellian distributions, are studied. The advantage of the concept of hypoequilibrium state in studying nonequilibrium trajectories is discussed.

This paper presents a nonequilibrium thermodynamic model for the relaxation of a local, isolated system in nonequilibrium using the principle of steepest entropy ascent (SEA), which can be expressed as a variational principle in thermodynamic state space. The model is able to arrive at the Onsager relations for such a system. Since no assumption of local equilibrium is made, the conjugate fluxes and forces are intrinsic to the subspaces of the system's state space and are defined using the concepts of hypoequilibrium state and nonequilibrium intensive properties, which describe the nonmutual equilibrium status between subspaces of the thermodynamic state space. The Onsager relations are shown to be a thermodynamic kinematic feature of the system independent of the specific details of the micromechanical dynamics. Two kinds of relaxation processes are studied with different constraints (i.e., conservation laws) corresponding to heat and mass diffusion. Linear behavior in the near-equilibrium region as well as nonlinear behavior in the far-from-equilibrium region are discussed. Thermodynamic relations in the equilibrium and near-equilibrium realm, including the Gibbs relation, the Clausius inequality, and the Onsager relations, are generalized to the far-from-equilibrium realm. The variational principle in the space spanned by the intrinsic conjugate fluxes and forces is expressed via the quadratic dissipation potential. As an application, the model is applied to the heat and mass diffusion of a system represented by a single-particle ensemble, which can also be applied to a simple system of many particles. Phenomenological transport coefficients are also derived in the near-equilibrium realm.

Traditional answers to what the 2nd Law is are well known. Some are based on the microstate of a system wandering rapidly through all accessible phase space, while others are based on the idea of a system occupying an initial multitude of states due to the inevitable imperfections of measurements that then effectively, in a coarse grained manner, grow in time (mixing). What has emerged are two somewhat less traditional approaches from which it is said that the 2nd Law emerges, namely, that of the theory of quantum open systems and that of the theory of typicality. These are the two principal approaches, which form the basis of what today has come to be called quantum thermodynamics. However, their dynamics remains strictly linear and unitary, and, as a number of recent publications have emphasized, “testing the unitary propagation of pure states alone cannot rule out a nonlinear propagation of mixtures”. Thus, a non-traditional approach to capturing such a propagation would be one which complements the postulates of QM by the 2nd Law of thermodynamics, resulting in a possibly meaningful, nonlinear dynamics. An unorthodox approach, which does just that, is intrinsic quantum thermodynamics and its mathematical framework, steepest-entropy-ascent quantum thermodynamics. The latter has evolved into an effective tool for modeling the dynamics of reactive and non-reactive systems at atomistic scales. It is the usefulness of this framework in the context of quantum thermodynamics as well as the theory of typicality which are discussed here in some detail. A brief discussion of some other trends such as those related to work, work extraction, and fluctuation theorems is also presented.

Detailed thermodynamic, kinetic, geometric, and cost models are developed, implemented, and validated for the synthesis/design and operational analysis of hybrid solid oxide fuel cell (SOFC)-gas turbine-steam turbine systems ranging in size from $1.5MWeto10MWe$. The fuel cell model used in this research work is based on a tubular Siemens-Westinghouse-type SOFC, which is integrated with a gas turbine and a heat recovery steam generator (HRSG) integrated in turn with a steam turbine cycle. The current work considers the possible benefits of using the exhaust gases in a HRSG in order to produce steam, which drives a steam turbine for additional power output. Four different steam turbine cycles are considered in this research work: a single-pressure, a dual-pressure, a triple-pressure, and a triple-pressure with reheat. The models have been developed to function both at design (full load) and off-design (partial load) conditions. In addition, different solid oxide fuel cell sizes are examined to assure a proper selection of SOFC size based on efficiency or cost. The thermoeconomic analysis includes cost functions developed specifically for the different system and component sizes (capacities) analyzed. A parametric study is used to determine the most viable system/component syntheses/designs based on maximizing the total system efficiency or minimizing the total system life cycle cost.