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The Rate-Controlled Constrained-Equilibrium Approach to Far-From-Local-Equilibrium Thermodynamics
Department of Mechanical and Industrial Engineering, Universita di Brescia, Brescia, 25123, Italy
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA
Department of Mechanical Engineering, Northeastern University Boston, MA 02115, USA
* Author to whom correspondence should be addressed.
Received: 12 October 2011; in revised form: 31 December 2011 / Accepted: 18 January 2012 / Published: 30 January 2012
Abstract: The Rate-Controlled Constrained-Equilibrium (RCCE) method for the description of the time-dependent behavior of dynamical systems in non-equilibrium states is a general, effective, physically based method for model order reduction that was originally developed in the framework of thermodynamics and chemical kinetics. A generalized mathematical formulation is presented here that allows including nonlinear constraints in non-local equilibrium systems characterized by the existence of a non-increasing Lyapunov functional under the system’s internal dynamics. The generalized formulation of RCCE enables to clarify the essentials of the method and the built-in general feature of thermodynamic consistency in the chemical kinetics context. In this paper, we work out the details of the method in a generalized mathematical-physics framework, but for definiteness we detail its well-known implementation in the traditional chemical kinetics framework. We detail proofs and spell out explicit functional dependences so as to bring out and clarify each underlying assumption of the method. In the standard context of chemical kinetics of ideal gas mixtures, we discuss the relations between the validity of the detailed balance condition off-equilibrium and the thermodynamic consistency of the method. We also discuss two examples of RCCE gas-phase combustion calculations to emphasize the constraint-dependent performance of the RCCE method.
Keywords: non-equilibrium and irreversible thermodynamics; nonlinear dynamics and nonlinear dynamical systems; nonlinear dynamics and nonlinear dynamical systems; chemical kinetics and dynamics
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Beretta, G.P.; Keck, J.C.; Janbozorgi, M.; Metghalchi, H. The Rate-Controlled Constrained-Equilibrium Approach to Far-From-Local-Equilibrium Thermodynamics. Entropy 2012, 14, 92-130.
Beretta GP, Keck JC, Janbozorgi M, Metghalchi H. The Rate-Controlled Constrained-Equilibrium Approach to Far-From-Local-Equilibrium Thermodynamics. Entropy. 2012; 14(2):92-130.
Beretta, Gian Paolo; Keck, James C.; Janbozorgi, Mohammad; Metghalchi, Hameed. 2012. "The Rate-Controlled Constrained-Equilibrium Approach to Far-From-Local-Equilibrium Thermodynamics." Entropy 14, no. 2: 92-130.