THERMAL PHYSICS: AN INTRODUCTION TO THERMODYNAMICS
CONTENTS WHAT IS STATISTICAL MECHANICS? EXERCISES QUANTUM DICE PROBABILITY DISTRIBUTIONS WAITING TIMES STIRLING’S APPROXIMATION STIRLING AND ASYMPTOTIC SERIES RANDOM MATRIX THEORY SIX DEGREES OF SEPARATION SATISFACTORY MAP COLORINGS RANDOM WALKS AND EMERGENT PROPERTIES RANDOM WALK EXAMPLES: UNIVERSALITY AND SCALE INVARIANCE THE DI?USION EQUATION CURRENTS AND EXTERNAL FORCES SOLVING THE DI?USION EQUATION FOURIER GREEN RANDOM WALKS IN GRADE SPACE PHOTON DI?USION IN THE SUN MOLECULAR MOTORS AND RANDOM WALKS PERFUME WALK GENERATING RANDOM WALKS FOURIER AND GREEN PERIODIC DI?USION THERMAL DI?USION FRYING PAN POLYMERS AND RANDOM WALKS STOCKS, VOLATILITY, AND DIVERSI?CATION COMPUTATIONAL ?NANCE: PRICING DERIVATIVES BUILDING A PERCOLATION NETWORK TEMPERATURE AND EQUILIBRIUM THE MICROCANONICAL ENSEMBLE THE MICROCANONICAL IDEAL GAS CON?GURATION SPACE MOMENTUM SPACE WHAT IS TEMPERATURE? PRESSURE AND CHEMICAL POTENTIAL ADVANCED TOPIC: PRESSURE IN MECHANICS AND STATIS- TICAL MECHANICS ENTROPY, THE IDEAL GAS, AND PHASE-SPACE RE?NEMENTS TEMPERATURE AND ENERGY LARGE AND VERY LARGE NUMBERS ESCAPE VELOCITY PRESSURE COMPUTATION HARD SPHERE GAS CONNECTING TWO MACROSCOPIC SYSTEMS GAS MIXTURE MICROCANONICAL ENERGY ?UCTUATIONS GAUSS AND POISSON TRIPLE PRODUCT RELATION MAXWELL RELATIONS SOLVING DI?ERENTIAL EQUATIONS: THE PENDULUM PHASE-SPACE DYNAMICS AND ERGODICITY LIOUVILLE’S THEOREM ERGODICITY EQUILIBRATION LIOUVILLE VS THE DAMPED PENDULUM INVARIANT MEASURES JUPITER! AND THE KAM THEOREM ENTROPY ENTROPY AS IRREVERSIBILITY: ENGINES AND THE HEAT DEATH OF THE UNIVERSE ENTROPY AS DISORDER ENTROPY OF MIXING: MAXWELL’S DEMON AND OSMOTIC PRESSURE RESIDUAL ENTROPY OF GLASSES: THE ROADS NOT TAKEN ENTROPY AS IGNORANCE: INFORMATION AND MEMORY NON-EQUILIBRIUM ENTROPY INFORMATION ENTROPY LIFE AND THE HEAT DEATH OF THE UNIVERSE BURNING INFORMATION AND MAXWELLIAN DEMONS REVERSIBLE COMPUTATION BLACK HOLE THERMODYNAMICS PRESSURE–VOLUME DIAGRAM CARNOT REFRIGERATOR DOES ENTROPY INCREASE? THE ARNOL’D CAT MAP CHAOS, LYAPUNOV, AND ENTROPY INCREASE ENTROPY INCREASES: DI?USION ENTROPY OF GLASSES RUBBER BAND HOW MANY SHU?ES? SHANNON ENTROPY FRACTAL DIMENSIONS DERIVING ENTROPY FREE ENERGIES THE CANONICAL ENSEMBLE UNCOUPLED SYSTEMS AND CANONICAL ENSEMBLES GRAND CANONICAL ENSEMBLE WHAT IS THERMODYNAMICS? MECHANICS: FRICTION AND ?UCTUATIONS CHEMICAL EQUILIBRIUM AND REACTION RATES FREE ENERGY DENSITY FOR THE IDEAL GAS EXPONENTIAL ATMOSPHERE TWO-STATE SYSTEM NEGATIVE TEMPERATURE MOLECULAR MOTORS AND FREE ENERGIES LAPLACE LAGRANGE LEGENDRE EULER GIBBS–DUHEM CLAUSIUS–CLAPEYRON BARRIER CROSSING MICHAELIS–MENTEN AND HILL POLLEN AND HARD SQUARES STATISTICAL MECHANICS AND STATISTICS QUANTUM STATISTICAL MECHANICS MIXED STATES AND DENSITY MATRICES ADVANCED TOPIC: DENSITY MATRICES QUANTUM HARMONIC OSCILLATOR BOSE AND FERMI STATISTICS NON-INTERACTING BOSONS AND FERMIONS MAXWELL–BOLTZMANN ‘QUANTUM’ STATISTICS BLACK-BODY RADIATION AND BOSE CONDENSATION FREE PARTICLES IN A BOX BLACK-BODY RADIATION BOSE CONDENSATION METALS AND THE FERMI GAS ENSEMBLES AND QUANTUM STATISTICS PHONONS AND PHOTONS ARE BOSONS PHASE-SPACE UNITS AND THE ZERO OF ENTROPY DOES ENTROPY INCREASE IN QUANTUM SYSTEMS? PHOTON DENSITY MATRICES SPIN DENSITY MATRIX LIGHT EMISSION AND ABSORPTION EINSTEIN’S A AND B BOSONS ARE GREGARIOUS: SUPER?UIDS AND LASERS CRYSTAL DEFECTS PHONONS ON A STRING SEMICONDUCTORS BOSE CONDENSATION IN A BAND BOSE CONDENSATION: THE EXPERIMENT THE PHOTON-DOMINATED UNIVERSE WHITE DWARFS, NEUTRON STARS, AND BLACK HOLES CALCULATION AND COMPUTATION THE ISING MODEL MAGNETISM BINARY ALLOYS LIQUIDS, GASES, AND THE CRITICAL POINT HOW TO SOLVE THE ISING MODEL MARKOV CHAINS WHAT IS A PHASE? PERTURBATION THEORY ISING ?UCTUATIONS AND SUSCEPTIBILITIES COIN ?IPS AND MARKOV RED AND GREEN BACTERIA DETAILED BALANCE METROPOLIS IMPLEMENTING ISING WOL? IMPLEMENTING WOL? STOCHASTIC CELLS THE REPRESSILATOR ENTROPY INCREASES! MARKOV CHAINS HYSTERESIS AND AVALANCHES HYSTERESIS ALGORITHMS NP-COMPLETENESS AND KSAT ORDER PARAMETERS, BROKEN SYMMETRY, AND TOPOLOGY IDENTIFY THE BROKEN SYMMETRY DE?NE THE ORDER PARAMETER EXAMINE THE ELEMENTARY EXCITATIONS CLASSIFY THE TOPOLOGICAL DEFECTS TOPOLOGICAL DEFECTS IN NEMATIC LIQUID CRYSTALS TOPOLOGICAL DEFECTS IN THE XY MODEL DEFECT ENERGETICS AND TOTAL DIVERGENCE TERMS DOMAIN WALLS IN MAGNETS LANDAU THEORY FOR THE ISING MODEL SYMMETRIES AND WAVE EQUATIONS SUPER?UID ORDER AND VORTICES SUPER?UIDS: DENSITY MATRICES AND ODLRO 10 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 ?UCTUATION-DISSIPATION THEOREM 10 9 CAUSALITY AND KRAMERS–KR¨ONIG MICROWAVE BACKGROUND RADIATION PAIR DISTRIBUTIONS AND MOLECULAR DYNAMICS DAMPED OSCILLATOR SPIN TELEGRAPH NOISE IN NANOJUNCTIONS FLUCTUATION-DISSIPATION: ISING NOISE AND LANGEVIN EQUATIONS MAGNETIC DYNAMICS QUASIPARTICLE POLES AND GOLDSTONE’S THEOREM 11 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 11 4 1 COARSENING 11 4 2 MARTENSITES 11 4 3 DENDRITIC GROWTH MAXWELL AND VAN DER WAALS THE VAN DER WAALS CRITICAL POINT INTERFACES AND VAN DER WAALS NUCLEATION IN THE ISING MODEL NUCLEATION OF DISLOCATION PAIRS COARSENING IN THE ISING MODEL ORIGAMI MICROSTRUCTURE MINIMIZING SEQUENCES AND MICROSTRUCTURE SNOW?AKES AND LINEAR STABILITY 12 CONTINUOUS PHASE TRANSITIONS 12 1 UNIVERSALITY 12 2 SCALE INVARIANCE 12 3 EXAMPLES OF CRITICAL POINTS 12 3 1 EQUILIBRIUM CRITICALITY: ENERGY VERSUS ENTROPY 12 3 2 QUANTUM CRITICALITY: ZERO-POINT ?UCTUATIONS VER- SUS ENERGY 12 3 3 DYNAMICAL SYSTEMS AND THE ONSET OF CHAOS 12 3 4 GLASSY SYSTEMS: RANDOM BUT FROZEN 12 3 5 PERSPECTIVES ISING SELF-SIMILARITY SCALING AND CORRECTIONS TO SCALING SCALING AND COARSENING BIFURCATION THEORY MEAN-?ELD THEORY THE ONSET OF LASING RENORMALIZATION-GROUP TRAJECTORIES SUPERCONDUCTIVITY AND THE RENORMALIZATION GROUP PERIOD DOUBLING THE RENORMALIZATION GROUP AND THE CENTRAL LIMIT THEOREM: SHORT THE RENORMALIZATION GROUP AND THE CENTRAL LIMIT THEOREM: LONG PERCOLATION AND UNIVERSALITY HYSTERESIS AND AVALANCHES: SCALING