Statistical Mechanics: Entropy, Order Parameters, and Complexity - James P. Sethna

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Résumé :

• 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??er-Rao


• 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: Maxwell-Boltzmann 'quantum' statistics


• 7.6: Black-body radiation and Bose condensation


• 7.7: Metals and the Fermi gas


• Calculation and computation


• 8.1: The Ising model


• 8.2: Markov chains


• 8.3: What is a phase? Perturbation theory


• Order parameters, broken symmetry, and topology


• 9.1: Identify the broken symmetry


• 9.2: Define the order parameter


• 9.3: Examine the elementary excitations


• 9.4: Classify the topological defects


• 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 fluctuation-dissipation theorem


• 10.9: Causality and Kramers-Kr??onig


• Abrupt phase transitions


• 11.1: Stable and metastable phases


• 11.2: Maxwell construction

  Biographie:
  

  • 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?er-Rao
  
  
  • 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: Maxwell-Boltzmann 'quantum' statistics
  
  
  • 7.6: Black-body radiation and Bose condensation
  
  
  • 7.7: Metals and the Fermi gas
  
  
  • Calculation and computation
  
  
  • 8.1: The Ising model
  
  
  • 8.2: Markov chains
  
  
  • 8.3: What is a phase? Perturbation theory
  
  
  • Order parameters, broken symmetry, and topology
  
  
  • 9.1: Identify the broken symmetry
  
  
  • 9.2: Define the order parameter
  
  
  • 9.3: Examine the elementary excitations
  
  
  • 9.4: Classify the topological defects
  
  
  • 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 fluctuation-dissipation theorem
  
  
  • 10.9: Causality and Kramers-Kr?onig
  
  
  • Abrupt phase transitions
  
  
  • 11.1: Stable and metastable phases
  
  
  • 11.2: Maxwell construction
  ...

  Sommaire:
  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'er-Rao; 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 Maxwell-Boltzmann 'quantum' statistics; 7.6 Black-body radiation and Bose condensation; 7.7 Metals and the Fermi gas; Calculation and computation; 8.1 The Ising model; 8.2 Markov chains; 8.3 What is a phase? Perturbation theory; Order parameters, broken symmetry, and topology; 9.1 Identify the broken symmetry; 9.2 Define the order parameter; 9.3 Examine the elementary excitations; 9.4 Classify the topological defects; 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 fluctuation-dissipation theorem; 10.9 Causality and Kramers-Kronig; 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