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What is A Dynamical Systems Theory of Thermodynamics about?

As discussed in Chapter 1, in this monograph we develop thermodynamic system models using large-scale nonlinear compartmental dynamical systems. The mathematical foundation for compartmental modeling is nonnegative dynamical systems theory [194, 415], which involves dynamical systems with nonnegative state variables. Since our thermodynamic state equations govern energy, volume, and mass flow between subsystems, it follows from physical arguments that nonnegative system energy, volume, and mass initial conditions give rise to dynamical system trajectories that remain in the nonnegative orthant of the state space. In this chapter, we introduce notation, several definitions, and some key results on nonlinear nonnegative dynamical systems needed for developing the main results of this monograph. In a definition or when a word is defined in the text, the concept defined is italicized. Italics in the running text are also used for emphasis. The definition of a word, phrase, or symbol is to be understood as an "if and only if" statement. Lower case letters such as x denote vectors, upper case letters such as A denote matrices, upper case script letters such as S denote sets, and lower ca

Author

Haddad, Wassim M.

Publisher

Princeton University Press

Published

2019

Language

EN

ISBN

9780691192598