A Dynamical Systems Theory of Thermodynamics /
Wassim M. Haddad.
- 1 online resource (774 pages)
- Princeton Series in Applied Mathematics .
- Princeton series in applied mathematics. .
Includes bibliographical references and index.
Chapter 1. Introduction; 1.1 An Overview of Classical Thermodynamics; 1.2 Thermodynamics and the Arrow of Time; 1.3 Modern Thermodynamics, Information Theory, and Statistical Energy Analysis; 1.4 Dynamical Systems; 1.5 Dynamical Thermodynamics: A Postmodern Approach; 1.6 A Brief Outline of the Monograph; Chapter 2. Dynamical Systems Theory; 2.1 Notation, Definitions, and Mathematical Preliminaries; 2.2 Stability Theory for Nonnegative Dynamical Systems; 2.3 Invariant Set Stability Theorems; 2.4 Semistability of Nonnegative Dynamical Systems2.5 Stability Theory for Linear Nonnegative Dynamical Systems; 2.6 Lyapunov Analysis for Continuum Dynamical Systems Defined by Semigroups; 2.7 Reversibility, Irreversibility, Recoverability, and Irrecoverability; 2.8 Output Reversibility in Dynamical Systems; 2.9 Reversible Dynamical Systems, Volume-Preserving Flows, and Poincar�e Recurrence; 2.10 Poincar�e Recurrence and Output Reversibility in Linear Dynamical Systems; Chapter 3. A Dynamical Systems Foundation for Thermodynamics; 3.1 Introduction 3.2 Conservation of Energy and the First Law of Thermodynamics3.3 Entropy and the Second Law of Thermodynamics; 3.4 Ectropy and the Second Law of Thermodynamics; 3.5 Semistability, Energy Equipartition, Irreversibility, and the Arrow of Time; 3.6 Entropy Increase and the Second Law of Thermodynamics; 3.7 Interconnections of Thermodynamic Systems; 3.8 Monotonicity of System Energies in Thermodynamic Processes; 3.9 The Second Law as a Statement of Entropy Increase; 3.10 Thermodynamic Systems with Linear Energy Exchange; 3.11 Semistability and Energy Equipartition in Linear Thermodynamic Models; 3.12 Semistability and Energy Equipartition of Thermodynamic Systems with Directed Energy FlowChapter 4. Temperature Equipartition and the Kinetic Theory of Gases; 4.1 Semistability and Temperature Equipartition; 4.2 Boltzmann Thermodynamics; 4.3 Connections to Classical Thermodynamic Energy, Entropy, and Thermal Equilibria; Chapter 5. Work, Heat, and the Carnot Cycle; 5.1 On the Equivalence of Work and Heat: The First Law Revisited; 5.2 Work Energy, Gibbs Free Energy, Helmholtz Free Energy, Enthalpy, and Entropy; 5.3 The Carnot Cycle and the Second Law of Thermodynamics; Chapter 6. Mass-Action Kinetics and Chemical Thermodynamics6.1 Introduction; 6.2 Reaction Networks; 6.3 The Law of Mass Action and the Kinetic Equations; 6.4 Nonnegativity of Solutions; 6.5 Realization of Mass-Action Kinetics; 6.6 Reducibility of the Kinetic Equations; 6.7 Stability Analysis of Linear and Nonlinear Kinetics; 6.8 The Zero-Deficiency Theorem; 6.9 Chemical Equilibria, Chemical Potential, and Chemical Thermodynamics; Chapter 7. Finite-Time Thermodynamics; 7.1 Introduction; 7.2 Finite-Time Semistability of Nonlinear Nonnegative Dynamical Systems
"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."--Provided by publisher