10820PHYS521000

統計力學一 Statistical Mechanics (I)

Instructor

• Prof. Pochung Chen
• R521, Physics building
• pcchen {at} phys {dot} nthu {dot} edu {dot} tw

Teaching Assistent

• 張宸瑜
• a4201598@gmail.com
• General II building, Room-B13

Textbooks

Main textbook

• Statistical Mechanics: Entropy, Order Parameter, and Complexity by James Sethna.

Other references

• An introduction to statistical mechanics and thermodynamics by Robert H. Swendsen.

Time

• R5R6R7.

Room

• R019, Physics building.

Grade (Letter grade)

• Exam-1 (35%)
• Exam-2 (35%)
• Homework (30%)

YouTube Playlists

• StatMech-I

LMS

• 統計力學一Statistical Mechanics (I)

  • How to turn in your homework online

Slack

• 10820phys521000.slack.com

Syllabus

Part-1

• Chapter 1: What is statistical mechanics?

• Chapter 3: Temperature and equilibrium

  • 3.1 The microcanonical ensemble
  • 3.2 The microcanonical ideal gas
  • 3.3 What is temperature?
  • 3.4 Pressure and chemical potential
  • 3.5 Entropy, the ideal gas, and phase-space refinements

• Chapter 2: Random walks and emergent properties

  • 2.1 Random walk examples: universality and scale invariance
  • 2.2 The diffusion equation
  • 2.3 Currents and external forces
  • 2.4 Solving the diffusion equation

• Chapter 5: Entropy

  • 5.1 Entropy as irreversibility: engines and the heat death of the Universe
  • 5.2 Entropy as disorder
  • 5.3 Entropy as ignorance: information and memory

• Chapter 6: Free energies

  • 6.1 The canonical ensemble
  • 6.2 Uncoupled systems and canonical ensembles
  • 6.3 Grand canonical ensemble
  • 6.4 What is thermodynamics?
  • 6.5 Mechanics: friction and fluctuations
  • 6.6 Chemical equilibrium and reaction

Part-2

• Chapter 7: Quantum statistical mechanics

  • 7.1 Mixed states and density matrices
  • 7.1.1 Advanced topic: density matrices.
  • 7.2 Quantum harmonic oscillator
  • 7.3 Bose and Fermi statistics
  • 7.4 Non-interacting bosons and fermions
  • 7.5 Maxwell–Boltzmann ‘quantum’ statistics
  • 7.6 Black-body radiation and Bose

    • 7.6.1 Free particles in a box
    • 7.6.2 Black-body radiation
    • 7.6.3 Bose condensation
  • 7.7 Metals and the Fermi gas
• Chapter 26: Ideal quantum gases (R. H. Swendsen)
• Chapter 27: Bose-Einstein statistics (R. H. Swendsen)
• Chapter 28: Fermi-Dirac statistics (R. H. Swendsen)
• Chapter 11: Abrupt phase transitions

  • 11.1 Stable and metastable phases
  • 11.2 Maxwell construction
• Chapter 17: Phase transitions (R. H. Swendsen)
• Chapter 12: Continuous phase transitions
• Chapter 8: Calculation and model (James Sethna)
• Chapter 30: Phase transition and the Ising model (R. H. Swendsen)

Exams

• Exam-1

  • 2.1, 2.2, 2.3.
  • 3.1, 3.2, 3.3, 3.4, 3.41, 3.5
  • 5.1, 5.2, 5.3.
  • 6.1, 6.2, 6.3, 6.4.
  • HW1, HW2, HW3, HW4.
  • Lecture notes.
• Exam-2

  • James Sethna

    • Chapter 7.1 to 7.6
    • Chapter 11.1, 11.2
  • R. H. Swendsen

    • Chapter 17, 26, 27, 28, 30

Weekly schedule

• Week 1: 3/5/2020

  • Introduction
  • 3.1 The microcanonical ensemble
  • 3.2 The microcanonical ideal gas
  • Note
• Week 2: 3/12/2020

  • 3.3 What is temperature?
  • 3.4 Pressure and chemical potential
  • 3.5 Entropy, the ideal gas, and phase-space refinements
  • Note
• Week 3: 3/19/2020

  • 3.5 Entropy, the ideal gas, and phase-space refinements
  • 2.1 Random walk examples: universality and scale invariance
  • 2.2 The diffusion equation
  • Note
• Week 4: 3/26/2020 YouTube Live

  • 5.1 Entropy as irreversibility: engines and the heat death of the Universe.
  • 5.2 Entropy as disorder.
  • 5.3 Entropy as ignorance: information and memory.
  • Note
  • HW1 due.
• Week 5: 4/2/2020 (No class)
• Week 6: 4/9/2020 YouTube Live

  • 6.1 The canonical ensemble.
  • 6.2 Uncoupled systems and canonical ensembles.
  • Note
  • HW2 due.
• Week 7: 4/16/2020 YouTube Live

  • 6.3 Grand canonical ensemble.
  • 6.4 What is thermodynamics?
  • Note
• Week 8: 4/23/2020 YouTube Live

  • HW3, due.
  • Note
• Week 9: 4/30/2020 YouTube Live

  • HW4 due.
  • Note
• Week 10: 5/7/2020

  • Exam-1
• Week 11: 5/14/2020

  • Ideal quantum gases (Swendsen)
  • Note
• Week 12: 5/21/2020

  • HW5 due.
  • Ideal quantum gases (Swendsen)
  • Bose-Einstein statistics
  • Note
• Week 13: 5/28/2020

  • Fermi-Dirac statistics
  • Note
• Week 14: 6/4/2020

  • Phase transitions
  • HW6 due.
  • Note
• Week 15: 6/11/2020

  • Phase transitions
• Week 16: 6/18/2020

  • HW7 due.
  • Exam-2

Homework

• HW1, due on 3/26/2020

  • Pb 1.4 (v2) Stirling's formula.
  • Pb 3.6 (v2) Connecting two macroscopic systems.
  • Pb 3.10 (v2) Triple product relation.
  • Pb 3.11 (v2) Maxwell relation.
• HW2, due on 4/9/2020

  • Pb 1.2 (v2) Probability distributions.
  • Pb 2.1 (v2) Random walks in grade space.
  • Pb 2.14 (v2) Modified random walk.
  • Pb 2.15 (v2) Diffusion and conserved particles.
  • Pb 5.4 (v2) Black hole thermodynamics.
• HW3, due on 4/16/2020 4/23/2020.
• HW4, due on 4/30/2020.
• HW5, due on 5/21/2020.
• HW6, due on 6/4/2020.
• HW7, due on 6/18/2020.