A Dynamical Systems Theory of Thermodynamics (Princeton Series in Applied Mathematics (68))

Description

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. Cover A Dynamical Systems Theory of Thermodynamic Copyright Dedication Epigraph Contents Preface 1 Introduction 2 Dynamical Systems Theory 3 A Dynamical Systems Foundation for Thermodynamics 4 Temperature Equipartition and the Kinetic Theory of Gases 5 Work, Heat, and the Carnot Cycle 6 Mass-Action Kinetics and Chemical Thermodynamics 7 Finite-Time Thermodynamics 8 Critical Phenomena and Continuous Phase Transitions 9 Thermodynamic Modeling of Discrete Dynamical Systems 10 Critical Phenomena and Discontinuous Phase Transitions 11 Continuum Thermodynamics 12 Stochastic Thermodynamics: A Dynamical Systems Approach 13 Relativistic Mechanics 14 Relativistic Thermodynamics 15 Thermodynamic Models with Subluminal Heat Propagation Speeds 16 Thermodynamic Models with Subluminal Heat Propagation Speeds 17 Epilogue 18 Afterword Bibliography Index