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Mathematical Foundations of Thermodynamics - 1st Edition - ISBN: 9780080100715, 9781483184913

Mathematical Foundations of Thermodynamics

1st Edition

International Series of Monographs on Pure and Applied Mathematics

Author: R. Giles
Editors: I. N. Sneddon M. Stark S. Ulam
eBook ISBN: 9781483184913
Imprint: Pergamon
Published Date: 1st January 1964
Page Count: 252
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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.

Table of Contents



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



Symbol Index


No. of pages:
© Pergamon 1964
1st January 1964
eBook ISBN:

About the Author

R. Giles

About the Editors

I. N. Sneddon

M. Stark

S. Ulam

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