Thermal Physics - Wyatt's Notes

sources:

• text: Halliday, Resnick, Walker - Fundamentals of Physics

graph TD
    T[Temperature] --> E[Energy]
    E --> S[Entropy]
    S --> Q[Heat Transfer]

1. The Laws of Thermodynamics
2. Statistical Mechanics
3. The Grand Canonical Ensemble
4. Fermi Gas at Finite Temperature
5. Bose-Einstein Condensation
6. The Ising Model
7. Classical Limit and the Maxwell-Boltzmann Distribution
8. Common Pitfalls
9. Problem Set
10. Phase Transitions
11. Landau Theory of Phase Transitions
12. Ising Model and Mean-Field Theory
13. Fluctuation-Dissipation Theorem
14. Microcanonical Ensemble
15. Quantum Statistics in Detail
16. The Debye Model of Solids
17. Thermodynamic Response Functions
18. Quantum Statistical Mechanics: Advanced Topics
19. Irreversible Thermodynamics and Fluctuations
20. Thermodynamics of Information Processing

University-level thermal physics notes covering thermodynamics, statistical mechanics, and phase transitions.

• Thermodynamics: Laws, entropy, free energy, thermodynamic potentials. The four laws of thermodynamics govern energy, entropy, and temperature — they apply to all physical systems.
• Statistical Mechanics: Ensembles, partition functions, quantum statistics. Statistical mechanics connects microscopic particle behaviour to macroscopic thermodynamic properties.
• Phase Transitions: Landau theory, mean-field theory, critical phenomena. Phase transitions (solid-liquid-gas, ferromagnetic) involve sudden changes in system properties.
• Advanced Topics: Fluctuation-dissipation theorem, irreversible thermodynamics. These extend thermodynamics to non-equilibrium systems.

• Classical mechanics (Newton”s laws, energy, momentum)
• Multivariable calculus (partial derivatives, integrals)
• Basic quantum mechanics (helpful but not required)
• Mathematical proofs and logic

Start with the laws of thermodynamics to build foundational knowledge, then progress to statistical mechanics and phase transitions. Each section includes worked examples and practice problems.

Use the sidebar to browse topics, or start with the introductory pages linked from the sidebar.

Each section includes:

• Detailed explanations of key concepts
• Worked examples with step-by-step solutions
• Practice problems with answers
• Common pitfalls and how to avoid them
• Connections to other areas of physics

1. Master the laws: Understand the four laws of thermodynamics and their implications. Zeroth: thermal equilibrium is transitive. First: energy conservation. Second: entropy increases. Third: absolute zero is unattainable.
2. Practise problems: Work through many problems to build intuition. Thermodynamics problems require careful identification of systems and processes.
3. Draw diagrams: Visualise phase diagrams and thermodynamic processes. PV diagrams show work done; TS diagrams show entropy changes.
4. Learn ensembles: Understand the microcanonical, canonical, and grand canonical ensembles. Each ensemble describes a different physical situation (isolated, thermal contact, particle exchange).
5. Connect to modern physics: Relate thermal physics to condensed matter and cosmology. Bose-Einstein condensation, neutron stars, and the cosmic microwave background all require thermal physics.

• Classical Mechanics: Newtonian mechanics underlying thermodynamics; kinetic theory connects microscopic motion to temperature.

• Solid State Physics: Statistical mechanics of solids; phonons and electronic heat capacity require thermal physics.

• Quantum Mechanics: Quantum statistics and thermal properties; Fermi-Dirac and Bose-Einstein distributions are quantum.

• Mathematics: Probability theory and combinatorics underpin statistical mechanics.

• Calculus

• Linear Algebra

• Vector Calculus

• Quantum Computing

Thermal physics bridges two seemingly disconnected descriptions of the same system: the macroscopic view (temperature, pressure, entropy, energy) and the microscopic view (individual atoms and molecules bouncing around according to Newton’s laws). The four laws of thermodynamics are empirical observations about energy, entropy, and temperature that apply to everything from engines to black holes. The zeroth law defines temperature. The first law is energy conservation. The second law — that entropy never decreases in an isolated system — is perhaps the most profound statement in physics: it gives time a direction and explains why heat flows from hot to cold, why you can’t unscramble an egg, and why perpetual motion machines are impossible.

Statistical mechanics explains why the thermodynamic laws hold by counting微观 states. The key insight is that entropy is a measure of how many microscopic configurations are consistent with the macroscopic state you observe. A gas fills the whole room because there are overwhelmingly more arrangements where molecules are spread out than arrangements where they’re clustered in a corner. The partition function — a single mathematical object — encodes all thermodynamic information about a system. From it you can derive temperature, pressure, heat capacity, magnetization, and everything else. The three ensembles (microcanonical, canonical, grand canonical) correspond to different physical situations: isolated systems, systems in thermal contact, and systems that exchange particles.

Phase transitions are where thermal physics becomes most dramatic. Water boiling, magnets losing their magnetism, superconductors appearing — these are all phase transitions where the macroscopic properties of a system change abruptly. Landau theory explains this through symmetry breaking: below the critical temperature, the system “chooses” a preferred state from among many equally valid options. Mean-field theory approximates the complex interactions between particles with an average effect, giving qualitatively correct phase diagrams. The fluctuation-dissipation theorem connects equilibrium fluctuations to response functions, bridging the gap between microscopic noise and macroscopic behaviour.