Statistical Mechanics

Preface Contents List of figures What is statistical mechanics? 1.1: Quantum dice and coins 1.2: Probability distributions 1.3: Waiting time paradox 1.4: Stirling>'s formula 1.5: Stirling and asymptotic series 1.6: Random matrix theory 1.7: Six degrees of separation 1.8: Satisfactory map colorings 1.9: First to fail: Weibull 1.10: Emergence 1.11: Emergent vs. fundamental 1.12: Self-propelled particles 1.13: The birthday problem 1.14: Width of the height distribution 1.15: Fisher information and Cram´erDSRao 1.16: Distances in probability space 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 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 Phase-space dynamics and ergodicity 4.1: Liouville>'s theorem 4.2: Ergodicity 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 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 rates 6.7: Free energy density for the ideal gas Quantum statistical mechanics 7.1: Mixed states and density matrices 7.2: Quantum harmonic oscillator 7.3: Bose and Fermi statistics 7.4: Non-interacting bosons and fermions 7.5: MaxwellDSBoltzmann 's regression hypothesis and time correlations 10.5: Susceptibility and linear response 10.6: Dissipation and the imaginary part 10.7: Static susceptibility 10.8: The fluctuation-dissipation theorem 10.9: Causality and KramersDSKr¨onig Abrupt phase transitions 11.1: Stable and metastable phases 11.2: Maxwell construction 11.3: Nucleation: critical droplet theory 11.4: Morphology of abrupt transitions Continuous phase transitions 12.1: Universality 12.2: Scale invariance 12.3: Examples of critical points A Appendix: Fourier methods A.1: Fourier conventions A.2: Derivatives, convolutions, and correlations A.3: Fourier methods and function space A.4: Fourier and translational symmetry References Index