Mathematical Foundations of Thermodynamics

Mathematical Foundations of Thermodynamics

International Series of Monographs on Pure and Applied Mathematics

1st Edition - January 1, 1964

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  • Author: R. Giles
  • eBook ISBN: 9781483184913

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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

  • Preface


    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

Product details

  • No. of pages: 252
  • Language: English
  • Copyright: © Pergamon 1964
  • Published: January 1, 1964
  • Imprint: Pergamon
  • eBook ISBN: 9781483184913

About the Author

R. Giles

About the Editors

I. N. Sneddon

M. Stark

S. Ulam

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