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.

• PrefaceContentsList of figuresWhat is statistical mechanics?1.1: Quantum dice and coins1.2: Probability distributions1.3: Waiting time paradox1.4: Stirling>'s formula1.5: Stirling and asymptotic series1.6: Random matrix theory1.7: Six degrees of separation1.8: Satisfactory map colorings1.9: First to fail: Weibull1.10: Emergence1.11: Emergent vs. fundamental1.12: Self-propelled particles1.13: The birthday problem1.14: Width of the height distribution1.15: Fisher information and Cram´erDSRao1.16: Distances in probability spaceRandom walks and emergent properties2.1: Random walk examples: universality and scale invariance2.2: The diffusion equation2.3: Currents and external forces2.4: Solving the diffusion equationTemperature and equilibrium3.1: The microcanonical ensemble3.2: The microcanonical ideal gas3.3: What is temperature?3.4: Pressure and chemical potential3.5: Entropy, the ideal gas, and phase-space refinementsPhase-space dynamics and ergodicity4.1: Liouville>'s theorem4.2: ErgodicityEntropy5.1: Entropy as irreversibility: engines and the heat death of the Universe5.2: Entropy as disorder5.3: Entropy as ignorance: information and memoryFree energies6.1: The canonical ensemble6.2: Uncoupled systems and canonical ensembles6.3: Grand canonical ensemble6.4: What is thermodynamics?6.5: Mechanics: friction and fluctuations6.6: Chemical equilibrium and reaction rates6.7: Free energy density for the ideal gasQuantum statistical mechanics7.1: Mixed states and density matrices7.2: Quantum harmonic oscillator7.3: Bose and Fermi statistics7.4: Non-interacting bosons and fermions7.5: MaxwellDSBoltzmann 's regression hypothesis and time correlations10.5: Susceptibility and linear response10.6: Dissipation and the imaginary part10.7: Static susceptibility10.8: The fluctuation-dissipation theorem10.9: Causality and KramersDSKr¨onigAbrupt phase transitions11.1: Stable and metastable phases11.2: Maxwell construction11.3: Nucleation: critical droplet theory11.4: Morphology of abrupt transitionsContinuous phase transitions12.1: Universality12.2: Scale invariance12.3: Examples of critical pointsA Appendix: Fourier methodsA.1: Fourier conventionsA.2: Derivatives, convolutions, and correlationsA.3: Fourier methods and function spaceA.4: Fourier and translational symmetryReferencesIndex

Review from previous edition Since the book treats intersections of mathematics, biology, engineering, computer science and social sciences, it will be of great help to researchers in these fields in making statistical mechanics useful and comprehensible. At the same time, the book will enrich the subject for physicists who'd like to apply their skills in other disciplines. [...] The author's style, although quite concentrated, is simple to understand, and has many lovely visual examples to accompany formal ideas and concepts, which makes the exposition live and intuitvely appealing.