Mathematical Foundations of Thermodynamics
International Series of Monographs on Pure and Applied Mathematics
Published on 22. January 2016
252 pages
978-1-4831-8491-3 (ISBN)
Description
Mathematical Foundations of Thermodynamics details the core concepts of the mathematical principles employed in thermodynamics. The book discusses the topics in a way that physical meanings are assigned to the theoretical terms. The coverage of the text includes the mechanical systems and adiabatic processes; topological considerations; and equilibrium states and potentials. The book also covers Galilean thermodynamics; symmetry in thermodynamics; and special relativistic thermodynamics. The book will be of great interest to practitioners and researchers of disciplines that deal with thermodynamics, such as physics, engineering, and chemistry.
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Content
PrefaceIntroductionChapter 1. Fundamental Concepts 1.1. The Structure of a Physical Theory 1.2. Primitive Observers 1.3. The Classical Formulations of Thermodynamics 1.4. Systems and States 1.5. Relations between States 1.6. The AxiomsChapter 2. Formal Processes 2.1. Definitions and Axioms 2.2. Addition of Processes 2.3. Ordering of Processes 2.4. Further Properties of ProcessesChapter 3. Components of Content 3.1. Definition 3.2. Existence of Components of ContentChapte 4. Irreversibility 4.1. Irreversibility Functions 4.2. The Construction of an Irreversibility Function 4.3. Irreversibility and EntropyChapter 5. Mechanical Systems and Adiabatic Processes 5.1. Physical Considerations 5.2. Mechanical States and Processes 5.3. Adiabatic ProcessesChapter 6. Entropy 6.1. Entropy Functions 6.2. The Construction of an Entropy FunctionChapter 7. Topological Considerations 7.1. Components of Content 7.2. EntropyChapter 8. Thermodynamic Space 8.1. Definitions 8.2. The Case of Finite Dimension 8.3. Mathematical CommentaryChapter 9. Equilibrium States and Potential 9.1. Equilibrium States 9.2. Components of PotentialChapter 10. Perfect Equilibrium States 10.1. Motivation 10.2. Properties of Perfect Equilibrium States 10.3. Perfect Thermodynamic SystemsChapter 11. Thermodynamics of a Rigidly Enclosed System 11.1. General Discussion 11.2. A Pathological Example 11.3. The Construction of an Energy Function 11.4. The Construction of an Entropy FunctionChapter 12. Systems of Variable Volume 12.1. Volume and Pressure 12.2. Simple SystemsChapter 13 . Electric and Magnetic Systems 13.1. Electrostatic Systems 13.2. Magnetic Systems 13.3. HysteresisChapter 14. Galilean Thermodynamics 14.1. The Components of Content 14.2. Galilean Transformations 14.3. The Equilibrium Surface 14.4. Properties of Equilibrium States 14.5. Thermodynamic Particles 14.6. Local Properties in an Equilibrium State 14.7. Some Special Cases 14.8. The Centrifugal EffectChapter 15. Symmetry in Thermodynamics 15.1. Introduction 15.2. The Principle of Equivalence 15.3. An Example 15.4. The Symmetry Group 15.5. The Transformation of States 15.6. The Transformation of Functions of StateChapter 16. Special Relativistic Thermodynamics 16.1. The Inhomogeneous Lorentz Group 16.2. The Components of Content 16.3. Rest Mass and Spin 16.4. The Representation of States in Space-Time 16.5. Center of Mass and Spin Angular Momentum 16.6. The Transformation of Entropy 16.7. Equilibrium States and Temperature 16.8. Local Properties of an Equilibrium State 16.9. ConclusionAppendix A. The Formal Theory A.l . Notation A.2. States and Processes A.3. Components of Content A.4. Quasi-Entropy A.5. The Duality Principle A.6. Boundedness A.7. Equilibrium States A.8. Potentials A.9. Absolute EntropyAppendix B. Subadditive Functions on a Group B.l . Partially Ordered Sets B.2. Subadditive Functions B.3. The Extension TheoremAppendix C. The Physical Basis for the Adjoint Representation C.l. The Case of Special Relativity C.2. The General CaseReferencesIndexSymbol Index
