ENTROPY-BASED PARAMETER ESTIMATION IN HYDROLOGY
CONTENTS WHAT IS STATISTICAL MECHANICS? EXERCISES QUANTUM DICE AND COINS PROBABILITY DISTRIBUTIONS WAITING TIME PARADOX STIRLING’S FORMULA STIRLING AND ASYMPTOTIC SERIES RANDOM MATRIX THEORY SIX DEGREES OF SEPARATION SATISFACTORY MAP COLORINGS FIRST TO FAIL: WEIBULL EMERGENCE EMERGENT VS FUNDAMENTAL SELF-PROPELLED PARTICLES WIDTH OF THE HEIGHT DISTRIBUTION FISHER INFORMATION AND CRAM´ER–RAO DISTANCES IN PROBABILITY SPACE 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 DRIFTING RANDOM WALK DI?USION OF NONCONSERVED PARTICLES DENSITY DEPENDENT DI?USION LOCAL CONSERVATION ABSORBING BOUNDARY CONDITIONS RUN & TUMBLE FLOCKING L´EVY ?IGHT CONTINUOUS TIME WALKS: BALLISTIC TO DI?USIVE RANDOM WALKS AND GENERATING FUNCTIONS TEMPERATURE AND EQUILIBRIUM THE MICROCANONICAL ENSEMBLE THE MICROCANONICAL IDEAL GAS CON?GURATION SPACE MOMENTUM SPACE WHAT IS TEMPERATURE? PRESSURE AND CHEMICAL POTENTIAL ENTROPY, THE IDEAL GAS, AND PHASE-SPACE RE?NEMENTS TEMPERATURE AND ENERGY LARGE AND VERY LARGE NUMBERS ESCAPE VELOCITY PRESSURE SIMULATION HARD SPHERE GAS CONNECTING TWO MACROSCOPIC SYSTEMS GAS MIXTURE MICROCANONICAL ENERGY ?UCTUATIONS GAUSS AND POISSON TRIPLE PRODUCT RELATION MAXWELL RELATIONS SOLVING THE PENDULUM WEIRDNESS IN HIGH DIMENSIONS PENDULUM ENERGY SHELL ENTROPY MAXIMUM AND TEMPERATURE TASTE, SMELL, AND µ UNDISTINGUISHED PARTICLES IDEAL GAS GLASS RANDOM ENERGY MODEL PHASE-SPACE DYNAMICS AND ERGODICITY LIOUVILLE’S THEOREM ERGODICITY EQUILIBRATION LIOUVILLE VS THE DAMPED PENDULUM INVARIANT MEASURES JUPITER! AND THE KAM THEOREM NO HAMILTONIAN ATTRACTORS PERVERSE INITIAL CONDITIONS CROOKS JARZYNSKI 2D TURBULENCE AND JUPITER’S GREAT RED SPOT 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 NONEQUILIBRIUM 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 ENTROPY OF SOCKS AGING, ENTROPY, AND DNA GRAVITY AND ENTROPY DATA COMPRESSION THE DYSON SPHERE ENTROPY OF THE GALAXY NUCLEOSYNTHESIS AND THE ARROW OF TIME EQUILIBRATION IN PHASE SPACE PHASE CONJUGATE MIRROR 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 GAS VS RUBBER BAND RUBBER BAND FREE ENERGY RUBBER BAND FORMALISM LANGEVIN DYNAMICS LANGEVIN SIMULATION GIBBS FOR PISTONS PISTONS IN PROBABILITY SPACE FIM FOR GIBBS CAN WE BURN INFORMATION? WORD FREQUENCIES: ZIPF’S LAW EPIDEMICS AND ZOMBIES NUCLEOSYNTHESIS AS A CHEMICAL REACTION QUANTUM STATISTICAL MECHANICS MIXED STATES AND DENSITY MATRICES QUANTUM HARMONIC OSCILLATOR BOSE AND FERMI STATISTICS NONINTERACTING 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 EIGENSTATE THERMALIZATION DRAWING WAVEFUNCTIONS MANY-FERMION WAVEFUNCTION NODES COOLING CO?EE THE GREENHOUSE E?ECT LIGHT BARYON SUPER?UIDS WHY ARE ATOMS CLASSICAL? IS SOUND A QUASIPARTICLE? QUANTUM MEASUREMENT AND ENTROPY ENTANGLEMENT OF TWO SPINS HEISENBERG ENTANGLEMENT 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 REPRESSILATOR ENTROPY INCREASES! MARKOV CHAINS HYSTERESIS AND AVALANCHES HYSTERESIS ALGORITHMS NP-COMPLETENESS AND KSAT ISING HARD DISKS ISING PARALLEL UPDATES ISING LOW TEMPERATURE EXPANSION 2D ISING CLUSTER EXPANSIONS UNICYCLE FRUIT ?IES AND MARKOV METASTABILITY AND MARKOV KINETIC PROOFREADING IN CELLS ORDER PARAMETERS, BROKEN SYMMETRY, AND TOPOLOGY IDENTIFY THE BROKEN SYMMETRY DE?NE THE ORDER PARAMETER EXAMINE THE ELEMENTARY EXCITATIONS CLASSIFY THE TOPOLOGICAL DEFECTS NEMATIC DEFECTS XY DEFECTS DEFECTS AND TOTAL DIVERGENCES DOMAIN WALLS IN MAGNETS LANDAU THEORY FOR THE ISING MODEL SYMMETRIES AND WAVE EQUATIONS SUPER?UID ORDER AND VORTICES SUPER?UIDS AND ODLRO ISING ORDER PARAMETER NEMATIC ORDER PARAMETER PENTAGONAL ORDER PARAMETER RIGIDITY OF CRYSTALS CHIRAL WAVE EQUATION SOUND AND GOLDSTONE’S THEOREM SUPER?UID SECOND SOUND CAN’T LASSO A BASKETBALL FINGERPRINTS DEFECTS IN CRYSTALS DEFECT ENTANGLEMENT NUMBER AND PHASE IN SUPER?UIDS 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 COSMIC MICROWAVE BACKGROUND RADIATION PAIR DISTRIBUTIONS AND MOLECULAR DYNAMICS DAMPED OSCILLATOR SPIN TELEGRAPH NOISE IN NANOJUNCTIONS FLUCTUATION-DISSIPATION: ISING NOISE AND LANGEVIN EQUATIONS MAGNET DYNAMICS QUASIPARTICLE POLES AND GOLDSTONE’S THEOREM HUMAN CORRELATIONS SUBWAY BENCH MONTE CARLO LIQUID FREE ENERGY ONSAGER REGRESSION HYPOTHESIS LIQUID DYNAMICS HARMONIC SUSCEPTIBILITY, DISSIPATION HARMONIC ?UCTUATION-DISSIPATION SUSCEPTIBILITIES AND CORRELATIONS HARMONIC KRAMERS–KR¨ONIG CRITICAL POINT RESPONSE 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 GIBBS FREE ENERGY BARRIER UNSTABLE TO WHAT? NUCLEATION IN 2D LINEAR STABILITY OF A GROWING INTERFACE NUCLEATION OF CRACKS ELASTIC THEORY DOES NOT CONVERGE MOSH PITS 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 AND THE RG RG AND THE CENTRAL LIMIT THEOREM: SHORT RG AND THE CENTRAL LIMIT THEOREM: LONG PERCOLATION AND UNIVERSALITY HYSTERESIS AND AVALANCHES: SCALING CRACKLING NOISES HEARING CHAOS PERIOD DOUBLING AND THE ONSET OF CHAOS THE GUTENBERG–RICHTER LAW RANDOM WALKS AND UNIVERSAL EXPONENTS DI?USION EQUATION AND UNIVERSAL SCALING FUNCTIONS HYSTERESIS AND BARKHAUSEN NOISE EARTHQUAKES AND WIRES ACTIVATED RATES AND THE SADDLE-NODE TRANSITION BIGGEST OF BUNCH: GUMBEL EXTREME VALUES: GUMBEL, WEIBULL, AND FR´ECHET CRITICAL CORRELATIONS ISING MEAN ?ELD DERIVATION MEAN-?ELD BOUND FOR FREE ENERGY AVALANCHE SIZE DISTRIBUTION THE ONSET OF CHAOS: LOWEST ORDER RG THE ONSET OF CHAOS: FULL RG SINGULAR CORRECTIONS TO SCALING CONFORMAL INVARIANCE PANDEMIC 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 SOUND WAVE FOURIER COSINES DOUBLE SINUSOID FOURIER GAUSSIANS UNCERTAINTY FOURIER RELATIONSHIPS ALIASING AND WINDOWING WHITE NOISE FOURIER MATCHING GIBBS PHENOMENON