Thermal Physics

5.

Statistical Mechanics

5.1.

Fundamental Concepts

5.1.1.

Microstates and Macrostates

5.1.1.1.

Definition of Microstates

5.1.1.2.

Definition of Macrostates

5.1.1.3.

5.1.2.

5.1.2.1.

Classical Phase Space

5.1.2.2.

Representation of States

5.1.2.3.

Liouville's Theorem

5.1.3.

Statistical Ensembles

5.1.3.1.

Concept of Ensembles

5.1.3.2.

Microcanonical Ensemble

5.1.3.2.1.

Definition and Characteristics

5.1.3.2.2.

Isolated Systems

5.1.3.3.

Canonical Ensemble

5.1.3.3.1.

Definition and Characteristics

5.1.3.3.2.

Systems in Thermal Contact

5.1.3.4.

Grand Canonical Ensemble

5.1.3.4.1.

Definition and Characteristics

5.1.3.4.2.

5.2.

The Statistical Basis of Entropy

5.2.1.

Boltzmann's Entropy Formula

5.2.1.1.

5.2.1.2.

Statistical Interpretation

5.2.2.

Connection to Thermodynamic Entropy

5.2.3.

Probabilistic Interpretation

5.2.4.

Information Theory Connections

5.3.

The Boltzmann Distribution

5.3.1.

Derivation of the Distribution

5.3.2.

Exponential Form

5.3.3.

Physical Interpretation

5.3.4.

Applications to Energy States

5.4.

The Partition Function

5.4.1.

Definition of Partition Function

5.4.2.

Canonical Partition Function

5.4.3.

Calculation Methods

5.4.4.

Relating Partition Function to Thermodynamics

5.4.4.1.

Internal Energy

5.4.4.2.

Helmholtz Free Energy

5.4.4.3.

5.4.4.4.

5.4.4.5.

5.4.5.

Examples and Applications

5.4.5.1.

Harmonic Oscillator

5.4.5.2.

Particle in a Box

5.4.5.3.

Rotational States

5.5.

Classical Statistical Mechanics

5.5.1.

Classical Limit

5.5.2.

Maxwell-Boltzmann Statistics

5.5.3.

Equipartition Theorem Revisited

5.6.

Quantum Statistical Mechanics

5.6.1.

Quantum States and Degeneracy

5.6.2.

Indistinguishability of Particles

5.6.3.

Symmetry Requirements

Previous

4. Kinetic Theory of Gases

Go to top

Next

6. Applications and Advanced Topics