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.

Contenu

Preface
Introduction
Chapter 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 Axioms
Chapter 2. Formal Processes
2.1. Definitions and Axioms
2.2. Addition of Processes
2.3. Ordering of Processes
2.4. Further Properties of Processes
Chapter 3. Components of Content
3.1. Definition
3.2. Existence of Components of Content
Chapte 4. Irreversibility
4.1. Irreversibility Functions
4.2. The Construction of an Irreversibility Function
4.3. Irreversibility and Entropy
Chapter 5. Mechanical Systems and Adiabatic Processes
5.1. Physical Considerations
5.2. Mechanical States and Processes
5.3. Adiabatic Processes
Chapter 6. Entropy
6.1. Entropy Functions
6.2. The Construction of an Entropy Function
Chapter 7. Topological Considerations
7.1. Components of Content
7.2. Entropy
Chapter 8. Thermodynamic Space
8.1. Definitions
8.2. The Case of Finite Dimension
8.3. Mathematical Commentary
Chapter 9. Equilibrium States and Potential
9.1. Equilibrium States
9.2. Components of Potential
Chapter 10. Perfect Equilibrium States
10.1. Motivation
10.2. Properties of Perfect Equilibrium States
10.3. Perfect Thermodynamic Systems
Chapter 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 Function
Chapter 12. Systems of Variable Volume
12.1. Volume and Pressure
12.2. Simple Systems
Chapter 13 . Electric and Magnetic Systems
13.1. Electrostatic Systems
13.2. Magnetic Systems
13.3. Hysteresis
Chapter 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 Effect
Chapter 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 State
Chapter 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. Conclusion
Appendix 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 Entropy
Appendix B. Subadditive Functions on a Group
B.l . Partially Ordered Sets
B.2. Subadditive Functions
B.3. The Extension Theorem
Appendix C. The Physical Basis for the Adjoint Representation
C.l. The Case of Special Relativity
C.2. The General Case
References
Index
Symbol Index