A Dynamical Systems Theory of Thermodynamics: (Princeton Series in Applied Mathematics)

A brand-new conceptual look at dynamical thermodynamics This book merges the two universalisms of thermodynamics and dynamical systems theory in a single compendium, with the latter providing an ideal language for the former, to develop a new and unique framework for dynamical thermodynamics. In particular, the book uses system-theoretic ideas to bring coherence, clarity, and precision to an important and poorly understood classical area of science. The dynamical systems formalism captures all of the key aspects of thermodynamics, including its fundamental laws, while providing a mathematically rigorous formulation for thermodynamical systems out of equilibrium by unifying the theory of mechanics with that of classical thermodynamics.This book includes topics on nonequilibrium irreversible thermodynamics, Boltzmann thermodynamics, mass-action kinetics and chemical reactions, finite-time thermodynamics, thermodynamic critical phenomena with continuous and discontinuous phase transitions, information theory, continuum and stochastic thermodynamics, and relativistic thermodynamics.A Dynamical Systems Theory of Thermodynamics develops a postmodern theory of thermodynamics as part of mathematical dynamical systems theory. The book establishes a clear nexus between thermodynamic irreversibility, the second law of thermodynamics, and the arrow of time to further unify discreteness and continuity, indeterminism and determinism, and quantum mechanics and general relativity in the pursuit of understanding the most fundamental property of the universe-the entropic arrow of time.

About the Author :
Wassim M. Haddad is a professor in the School of Aerospace Engineering, the David Lewis Chair in Dynamical Systems and Control, and chair of the Flight Mechanics and Control Discipline, all at the Georgia Institute of Technology, where he also holds a joint appointment in the School of Electrical and Computer Engineering. He is the coauthor of numerous books, including Stability and Control of Large-Scale Dynamical Systems and Nonlinear Dynamical Systems and Control (both Princeton).

Review :
“This remarkable book studies thermodynamics within the framework of dynamical systems theory. A major contribution by any standard, it is a gem in the tiara of books being written by one of the most prolific, deep-thinking, and insightful researchers working today.”—Frank Lewis, University of Texas, Arlington “Haddad develops an original mathematical framework for thermodynamics deeply rooted in modern systems theory, threading postulates and analyses of a science that has evolved from the seemingly mundane quest for efficiency in steam engines to the flow of time and the workings of the cosmos and life itself. He succeeds in presenting an all-encompassing treatise, from the early works of Carnot and Clausius to the insights of relativity and the conundrum of the time arrow, in a lucid exposition that systematically details a rigorous base for future generations of scientists and theorists.”—Tryphon Georgiou, University of California, Irvine "By applying ideas and techniques from compartmental systems theory, Haddad’s treatise places thermodynamics on a solid foundation for the twenty-first century."—Dennis Bernstein, University of Michigan "This effective blend of thermodynamics and the theory of dynamical systems provides a unified, coherent, and mathematically accurate framework that is currently missing in the literature. This is a significant contribution to several fields spanning dynamical systems, mathematics, physics, chemistry, and more. It will provide the underlying foundation for additional research and conceptual understanding of physical phenomena."—Kyriakos G. Vamvoudakis, Georgia Institute of Technology