Connection between statistics and thermodynamics; Concept of microstates phase space and its connection to Entropy; Classical Ideal Gas and the Maxwell Boltzmann Distribution, Entropy of mixing and Gibbs Paradox; Liouvilles Theorem, Microcanonical Ensemble, Canonical Ensemble and Partition Function calculation for various systems; Energy fluctuations in the Canonical Ensemble; Grand Canonical Ensemble; Number Density and Energy Fluctuations in the Grand Canonical ensemble; Quantum Statistics and calculation of the Density matrix for various systems; Indistinguishability of Particles, Symmetric and Anti-Symmetric wave functions and calculation of the the Bose-Einstein and Fermi-Dirac Distribution for a quantum Ideal Gas; Thermodynamic behaviour of an Ideal Bose Gas, Black-Body radiation and other applications of Bose-Einstein statistics; Thermodynamic behaviour of an ideal Fermi gas and various applications of Fermi-Dirac statistics such as Pauli paramagnetism and calculation of Chandasekhar limit in White Dwarf stars; Cluster expansion techniques for interacting systems; Introduction to basic ideas of phase transitions via Ising model and Van der Waals gas, exact solution of the Ising model in 1D; Boltzmanns Equation and the H-Theorem; Description of Einstein-Smoluchowski theory of Brownian motion as a stochastic process; Basic ideas behind the Fokker-Planck and Master equations with simple examples. |