Correlations and Entropy in Classical Statistical Mechanics - ISBN:0000000000

Correlations and Entropy in Classical Statistical Mechanics

Date: 21 April 2011, 12:00

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Contents
I INrRODUCTlON
NOTE ON NOTATION PROBABILITY DENSITIES AND THEIR EVOLUTION
1.1. Probability densities and averages
1.2. Molecular density
1.3. Double density
1.4. Examples of calculations of averages
1.5. Microscopic quantities
1.6. Intermolecular pressure
1.7. Liouville equation
1.8. Time derivatives
1.9. Chain of recurrence equations of motion
1.10. Diffusion equations
Conclusions
CHAPTER 2. OCCUPATION
2.1. Uncertainty in the number of particles present
2.2. Densities
2.3. Calculation of averages
2.4. Evolution
2.5. Analysis of correlations
2.6. The cumulant method
2.7. Perfect fluid
2.8. Molecular disorder
2.9. Pressure in a plasma
2.10. Mixtures
2.11. Mixtures. The case of a plasma
CHAPTER 3. STATISTICAL ENTROPY
3.1. Decoupling of a system
3.2. Definition of entropy
3.3. Fundamental inequalities for the entropy
3.4. Evolution of statistical entropy
3.5. Entropy of a system of identical particles
3.6. Entropy of a perfect fluid
3.7. Fundamental inequality for coupled systems
3.8. Entropy expressed as a function of reduced densities
3.9. Applications
CHAPTER 4. CANONICAL LAWS OF THERMODYNAMIC EQUILIBRIUM
4.1. Introduction
4.2. Mierocanonical equilibrium
4.3. Canonical equilibrium
4.4. Grand canonical equilibrium
4.5. Neutral equilibria
CHAPTER 5. THERMAL EQUILIBRIUM: SYSTEM OF IDENTICAL POINT MOLECULES
5.1. Canonical distribution 85
5.2. Grand canonical distribution and partition function 88
5.3. Densities as a function of alpha
5.4. Applied energy variations 90
5.5. hi, h12 , ... 91
5.6. Recurrence equations of the second kind and thermalization 92
5.7. Effects of a variation of the volume 95
CHAPTER 6. FINE STRUcrURE IN THERMAL EQUILIBRIUM 97
6.1. Fine structure equation 97
6.2. Grand partition function 101
6.3. Density distribution 102
6.4. The case of uniform media 104
6.5. Uniform medium fluctuations 109
6.6. Experimental determination of the fine-grained structure 111
6.7. Van der Waals equation of state 113
6.8. Second virial coefficient 116
6.9. Various calculations 118
CHAPTER 7. PHASE CHANGES
7.1. Condensation
7.2. Critical point
7.3. Surface tension
CHAPTER 8. THERMAL WAVES IN FLUIDS
8.1. Introduction
8.2. Density waves
8.3. Momentum
8.4. Energy
8.5. Thermodynamic interpretation
8.6. Higher-order moments
CHAPTER 9. ENTROPY AND HEAT
9.1. Introduction
9.2. Evolution of statistical entropy of an isolated system
9.3. The H-theorem
9.4. Statistical entropy density
9.5. Thermal entropy
REFERENCES
EXERCISES
INDEX

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