Front Matter Front Matter - Assessment Scheme, Academic honesty, TAs, Tips for learning Stat Mech, and Assignment Policy Course Learning Outcomes Time Table and TA consultation hours Reference book list and books reserved in University Library Lecture Notes Chapter 1 - What is statistical mechanics and why we need it? Coverage of our course and learning outcomes Chapter 1 Appendix - Brief history and some big names Class work in Week 1 - Uniform spatial distribution of molecules Class work in Week 1 - Key Results Class work in Week 1 Appendix A - Gaussian distribution function Class work in Week 1 - Extension (Optional) - Central Limit Theorem Chapter 2 - Short review on essential thermodynamics Chapter 2 Appendix A - Natural variables of thermodynamic functions Chapter 2 Appendix B - Legendre transformation and its graphical interpretation Chapter 3 Part 1 - Macrostate, Accessible Microstates and distributions in isolated system, Postulate of Equal a priori probabilities Chapter 3 Part 2 - Microcanonical Ensemble, Time average versus ensemble average, properly choosing members of an ensemble Chapter 3 Part 3 - Boltzmann's formula S = k ln W and what is W, the most probable distribution Chapter 3 Appendices A and B - Phase space (Gamma-space and mu-space), Stirling formula for ln N! Chapter 4 Part 1 - Physics and applications of S=k ln W - The formula makes sense, irreversible processes and arrow of time Chapter 4 Part 2 - Two systems in contact and thermodynamic results, S=k ln W re-interpreted as an average over ensemble members, Gibbs entropy formula Chapter 4 Appendix A - Schottky Defects in solids and related problems Chapter 4 Appendix B - Classical Ideal Gas (Microcanonical Ensemble) Chapter 4 Appendices C and D - Volume of D-dimensional Sphere and a List of standard problems Chapter 4 Appendix E (Optional) - Entropy of classical ideal gas entirely based on thermodynamics Chapter 4 Appendix F - What is W in N-particle quantum systems and What are single-particle states? Chapter 5 Part 1 - System in thermal equilibrium with a heat bath - Defining the problem, the Boltzmann Distribution and the Partition Function Z(T,V,N) Chapter 5 Part 2 - The Partition Function, Connecting Z to thermodynamic quantities, Canonical Ensemble - Concepts Chapter 5 Appendix (Optional) - Gaussian form of probability of finding system at energy E near the most probable value Chapter 6 Part 1 - Statistical Physics of Typical Systems (Canonical Ensemble) - Two-level systems (General treatment) Chapter 6 Part 2 - Paramagnetism (Essential Background on magnetism, J=1/2 as special case of two-level systems, General J case and Brillouin functions) Chapter 6 Part 3 - Classical (Langevin) theory of paramagnetism (ignoring quantization of z-component of magnetic moments) Chapter 6 Part 4 - Statistical physics of harmonic oscillators and heat capacity of solids Chapter 6 Part 5 - Statistical physics of vibrational and rotational motions in molecules Chapter 6 Part 6 - Ideal quantum gases within canonical ensemble (formalism, difficulties and way out) Chapter 7 Part 1 - Fermi-Dirac and Bose-Einstein distributions as the most probable distributions Chapter 7 Part 2 - Maxwell-Boltzmann distribution for classical particles as a by-product Chapter 7 Part 3 - Key results and summary on the most probable distribution approach Chapter 7 Appendix (Optional) - Re-deriving Boltzmann distribution and Partition Function using Lagrange Multipliers method Chapter 8 - Density of single-particle states (General Approach) Chapter 9 Part 1 - Classical Statistical Mechanics and standard applications Chapter 9 Part 2 - Nonideal gases (Phenomena - Phase diagram, Real gases, Interactions) Chapter 9 Part 3 - Non-ideal classical gas (Partition function and second virial coefficient) [lead sheet] Chapter 9 Part 3 - Non-ideal classical gas (second virial coefficient, van der Waals equation of state) Chapter 9 Part 4 - Van der Waals equation of state, first order phase transitions, critical point, law of corresponding state Chapter 9 Part 5 - Critical Phenomena - A first encounter (Phenomena near critical point, order parameter, power laws, critical exponents) Chapter 10 Part 1 - Critical Phenomena and Ferromagnetism (Phenomena of Ferromagnetism and Ising Model) Chapter 10 Part 2 - Critical Phenomena and Ferromagnetism (Mean field Theory of Ising Model - Physical Idea) Chapter 10 Part 3 - Critical Phenomena and Ferromagnetism (Mean Field Theory - critical exponents and formal approach) Chapter 10 Part 4 - Critical Phenomena (Free energy as a function of m and Landau Theory of Continuous Phase Transition) Chapter 10 Appendix A - The Percolation Problem Chapter 10 Appendix B (Optional) - Metropolis Monte Carlo Algorithm of Ising Model Chapter 10 Appendix C - Landau (Phenomenological) Theory of Continuous Transitions Chapter 10 Appendix D (Optional) - The origin of J in the Ising model (the exchange interaction) Chapter 11 - Grand Canonical Ensemble Theory (Systems with T,V,mu, Grand Partition Function, physics meaning, grand potential and connection to thermodynamics) Intermission - Lead Sheets into Chapter 12 (Re-deriving Fermi-Dirac and Bose-Einstein distributions)
