
Statistical Mechanics: Entropy, Order Parameters, and Complexity
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Content
- 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¿er-Rao
- 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: Maxwell-Boltzmann 'quantum' statistics
- 7.6: Black-body radiation and Bose condensation
- 7.7: Metals and the Fermi gas
- Calculation and computation
- 8.1: The Ising model
- 8.2: Markov chains
- 8.3: What is a phase? Perturbation theory
- Order parameters, broken symmetry, and topology
- 9.1: Identify the broken symmetry
- 9.2: Define the order parameter
- 9.3: Examine the elementary excitations
- 9.4: Classify the topological defects
- Correlations, response, and dissipation
- 10.1: Correlation functions: motivation
- 10.2: Experimental probes of correlations
- 10.3: Equal-time correlations in the ideal gas
- 10.4: Onsager'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 Kramers-Kr¿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
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