Statistical mechanics : entropy, order parameters, and complexity

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 CramerDSRao1.16: 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 KramersDSKronigAbrupt 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