Study notes for Statistical Physics A concise, unified overview of the subject - Info and Reading Options

"Study notes for Statistical Physics A concise, unified overview of the subject" Table Of Contents:

• 1- Content
• 2- 1. Introduction
• 3- 1.1. The isolated assembly
• 4- 1.2. Method of the most probable distribution
• 5- 1.3. Ensemble of assemblies: relationship between Gibbs and Boltzmann entropies
• 6- 2. Stationary ensembles
• 7- 2.1. Types of ensemble
• 8- 2.2. Variational method for the most probable distribution
• 9- 2.3. Canonical ensemble
• 10- 2.4. Compression of a perfect gas
• 11- 2.5. The Grand Canonical Ensemble (GCE)
• 12- 3. Examples of stationary ensembles
• 13- 3.1. Assembly of distinguishable particles
• 14- 3.2. Assembly of nonconserved, indistinguishable particles
• 15- 3.3. Conserved particles: general treatment for Bose-Einstein and Fermi-Dirac statistics
• 16- 3.4. The Classical Limit: Boltzmann Statistics
• 17- 4. The bedrock problem: strong interactions
• 18- 4.1. The interaction Hamiltonian
• 19- 4.2. Diagonal forms of the Hamiltonian
• 20- 4.3. Theory of specific heats of solids
• 21- 4.4. Quasi-particles and renormalization
• 22- 4.5. Perturbation theory for low densities
• 23- 4.6. The Debye-Hückel theory of the electron gas
• 24- 5. Phase transitions
• 25- 5.1. Critical exponents
• 26- 5.2. The ferro-paramagnetic transition
• 27- 5.3. The Weiss theory of ferromagnetism
• 28- 5.4. Macroscopic mean field theory: the Landau model for phase transitions
• 29- 5.5. Theoretical models
• 30- 5.6. The Ising model
• 31- 5.7. Mean-field theory with a variational principle
• 32- 5.8. Mean-field critical exponents for the Ising model
• 33- 6. Classical treatment of the Hamiltonian N-body assembly
• 34- 6.1. Hamilton’s equations and phase space
• 35- 6.2. Hamilton’s equations and 6N-dimensional phase space
• 36- 6.3. Liouville’s theorem for N particles in a box
• 37- 6.4. Probability density as a fluid
• 38- 6.5. Liouville’s equation: operator formalism
• 39- 6.6. The generalised H-theorem (due to Gibbs)
• 40- 6.7. Reduced probability distributions
• 41- 6.8. Basic cells in Γ space
• 42- 7. Derivation of transport equations
• 43- 7.1. BBGKY hierarchy (Born, Bogoliubov, Green, Kirkwood, Yvon)
• 44- 7.2. Equations for the reduced distribution functions
• 45- 7.3. The kinetic equation
• 46- 7.4. The Boltzmann equation
• 47- 7.5. The Boltzmann H-theorem
• 48- 7.6. Macroscopic balance equations
• 49- 8. Dynamics of Fluctuations
• 50- 8.1. Brownian motion and the Langevin equation
• 51- 8.2. Fluctuation-dissipation relations
• 52- 8.3. The response (or Green) function
• 53- 8.4. General derivation of the fluctuation-dissipation theorem
• 54- 9. Quantum dynamics
• 55- 9.1. Fermi’s master equation
• 56- 9.2. Applications of the master equation
• 57- 10. Consequences of time-reversal symmetry
• 58- 10.1. Detailed balance
• 59- 10.2. Dynamics of fluctuations
• 60- 10.3. Onsager’s theorem

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