Thermal physics: entropy and free energies

Preface

1. Introduction to Thermal Physics

1.1. Bird's-Eye view of Thermal Physics

2. All you Need to Know to Read the Rest of the Book

2.1. Several Taylor Series Expansions (*)

2.2. The Dirac δ Function (**)

2.3. Gamma Function (***)

2.4. The Gaussian Integrals (***)

2.5. Hypersphere in d-Dimensional Space (***)

2.6. Fourier Transformations (**)

2.7. Functional Derivative (**)

2.8. The Method of Undetermined Lagrange Multiplier (*)

2.9. Permutations Combinatorial and Arrangements (*)

2.10. Distribution Function (***)

2.11. The Central Limit Theorem (***)

2.12. Quantum Mechanics (***)

2.13. Thermal Physics on Computer

3. Isolated Thermal Systems

3.1. Introduction

3.2. The Fundamental Postulate

3.3. The Microcanonical Ensemble

3.4. Entropy and the Second Law of Thermodynamics

3.5. Entropy of Ideal Gas Mobile Particles

3.5.1. With Position- and Momentum-Definite Microstates

3.5.2. With Energy-Definite Microstates

3.6. The Fundamental Thermodynamic Equations

3.7. Temperature, Pressure and Chemical Potential

3.8. The Approach to Equilibrium

3.8.1. Temperature

3.8.2. Pressure

3.8.3. Chemical Potential

3.8.4. Multiple Traffic Control Systems

3.8.5. Some Reflections

3.9. Macrostates

3.9.1. The Largest Macrostate

3.9.2. How Dominant?

3.10. First Law of Thermodynamics

3.11. Extensive and Intensive Variables

3.12. Entropy of Mixing

3.13. Entropy-Driven Forces

3.13.1. Rubber Bands

3.13.2. Colloidal suspensions

3.13.3. Osmosis

3.13.4. Ideal Gas

3.14. Non-Mobile Thermal Systems

3.14.1. Magnets

3.14.2. Negative Temperature

3.15. Rubger Bands

3.16. Schottky Defects

4. Systems in Contact with a Thermal Reservior

4.1. Introduction

4.2. Helmholtz Free Energy

4.3. The Minimum Free Energy Principle

4.4. The Modified Postulate and the Boltzmann Factor

4.5. Response Functions and Fluctuations

4.5.1. Energy

4.5.2. Magnetization

4.6. Canonical Ensemble

4.6.1. Ising Spins

4.6.2. Schottky Defects

4.6.3. Ideal Gas

4.6.4. Equipartition Theorem

4.7. Maxwell-Boltzmann Distribution

4.8. Maxwell Velocity Distribution

4.9. Specific Heat and Einstein's Solid

4.10. Specific Heat and Debye's Solid

4.11. Solids and Gas in Equilibrium

4.12. Black Body Radiation

5. Entropy as a Measure of Disorder

5.1. Introduction

5.2. Order and Disorder

5.2. Uncertainity and Missing Information: Shannon's Entropy and Information Theory

5.4. Disorder Verses Uncertainty

6. Open Systems Exposed to Heat and Particle Reservoir

6.1. Introduction

6.2. Open Systems

6.3. Grand Canonical Ensemble Formalism

6.4. Hemoglobin and Myoglobin

7. Flexible Systems: Systems in Contact with Heat and Volume Reservoir

7.1. Introduction

7.2. Gibbs Free Energy

7.3. Constant Pressure Ensemble Formalism

7.3.1. Constant Pressure Ensemble Formalism I

7.3.2. Constant Pressure Ensemble Formalism I

7.4. Weak Solutions and Osmosis

7.5. External Chemcial Potential

8. Two More Energy-Like Functions and Concluding Remarks

8.1. Introdution

8.2. Energy

8.3. Enthalpy

8.4. Extensivities of Free Energies

8.5. Do Free Energies Have a Physical Meaning on Their Own? Maximum (Minimum) Work Theorem and Thermodynamic Potential

9. Quantum Ideal Gas

9.1. Introdution

9.2. The Occupation Number Formalism and Slightly Degenerate Ideal Gas

9.3. Fermi-Dirac and Bose-Einstein Distribution Functions

9.4. Degenerate Electron Gas Near and At T = 0

9.5. Degenerate Ideal Boson Gas At and Near T=0

9.6. The Classical Regime Revisited

10. Thermodynamics

10.1. Introduction

10.2. Carnot Heat Enging I

10.3. Carnot Heat Engine II

10.4. Relationships Between Thermodynamic Derivatives

10.5. Important Thermodynamic Derivatives and Their Mutual Relationships

10.6. Thermodynamic Stability

11. Energy Versus Free Energy

11.1. Introduction

11.2. Boltzmann Factor for Macrostates and Macrostate Free Energy

11.3. Thermodynamic Work and Thermodynamic Potential

11.4. Is Some Energy Really Free?

12. Phases and Phase Transitions

12.1. Introduction

12.2. Liquid State and Solid State

12.3. Phase Diagrams

12.4. Phase Rule

12.5. Coexistence Curves

12.6. Interface

12.7. The Van der Waals Theory

12.8. Dynamics of First Order Phase Transitions

12.8.1. Unstable Region

12.8.2. Metastable Region

12.9. Binary Systems: Mixing and Demixing

12.9. More on Binary Mixtures: Their Phase Equilibria

13. Second-Order Phase Transitions

13.1. Introduction

13.2. Liquid-Gas Molecular Systems

13.3. Spin Systems

13.3.1. Broken Symmetry, Order Parameter

13.4. Universality

13.5. Susceptibility and Spatial Correlations

13.6. Interacting Ising Spins on a Chain

13.7. Mean-Field Theory: Magnetism

13.8. Mean Field Theory: Liquid-Gas Sytems

13.9. Landau Mean Field Theory

13.10. The Static Scaling Hyposthesis

14. Landau-Ginzburg Free Energy Functional and Applications

14.1. Introduction

14.2. Landau-Ginzburg Free Engergy

14.3. The Renormalization Group Theory

14.4. Phase Separation Dynamics

14.4.1. The Time Evolution of the Order Parameter Function

15. Quantum Fluid

15.1. Introduction

15.2. Superfluidity

15.3. Bose-Einstein Codensation

16. Computer Simulations

16.1. Introdution

16.2. Monte Carlo Method I

16.3. Monte Carlo Method II: The Master Equation

16.4. Finite Size Scaling

Bibliography

Index