Chapter 2: Statistical Mechanics

The following sections are included:

• State Space

  • Fig. 2.1: Fermi function

  • Fig. 2.2: Boltzmann law

  • Figs. 2.3-2.4: Fermi function from Boltzmann law

  • Figs. 2.5-2.7: Two non-interacting energy levels

  • Fig. 2.8: Two levels with interaction

  • Quiz

• Boltzmann Law

  • Fig. 2.9: System and reservoir

  • Figs. 2.10-2.13: Justifying the law

  • Fig. 2.14: Canonical ensemble

  • Fig. 2.15: Grand canonical ensemble

  • Quiz

• Entropy

  • Figs. 2.16-2.18: Entropy from reservoir model

  • Figs. 2.19-2.20: Thermodynamic versus information entropy

  • Figs. 2.21-2.22: Reservoir model with d-level units

  • Fig. 2.23: μ, T from entropy S

  • Quiz

• Free Energy

  • Fig. 2.24: Free energy, F

  • Fig. 2.25: Gibbs’ inequality

  • Fig. 2.26: Equilibrium free energy

  • Figs. 2.27-2.28: Entropy drives flow

  • Quiz

• Self-Consistent Field

  • Figs. 2.29-2.32: The exponential problem

  • Figs. 2.33-2.36: SCF method

  • Fig. 2.37: SCF and neural networks

  • Quiz

• Fig. 2.38: 5-minute Summary