A Dynamical Systems Theory of Thermodynamics

Wassim M. Haddad

iyn 2019 · Princeton University Press

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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.

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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).