PHYS 5310 delves into the theoretical foundations of statistical mechanics, focusing on the statistical description of systems composed of a large number of particles. Key topics typically include: Ensemble Theory: Microcanonical, canonical, and grand canonical ensembles. Classical and Quantum Statistics: Maxwell-Boltzmann, Bose-Einstein, and Fermi-Dirac distributions. Partition Functions: Calculation and applications to thermodynamic quantities. Applications: Ideal gases, blackbody radiation, and phase transitions. This course also covers Fundamental principles of statistical mechanics, Liouville theorem, entropy, Fermi-Dirac distribution, Bose-Einstein distribution, Einstein condensation, density matrix, quantum statistical mechanics, kinetic methods, and transport theory.