Statistical Mechanics: Entropy, Order Parameters, and Complexity

James P. Sethna is professor of physics at Cornell University. Sethna has used statistical mechanics to make substantive contributions in a bewildering variety of subjects -- mathematics (dynamical systems and the onset of chaos), engineering (microstructure, plasticity, and fracture), statistics (information geometry, sloppy models, low-dimensional embeddings), materials science (glasses and spin glasses, liquid crystals, crackling noise, superconductivity), and popular culture (mosh pit dynamics and zombie outbreak epidemiology). He has collected cool, illustrative problems from students and colleagues over the decades, which inspired this textbook.

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