Basic Statistical Mechanics

In order to understand natural phenomena like phase transitions or nucleation or many biological reactions like protein folding, enzyme kinetics, we need to understand how many particles interact and behave together in certain specified manner. For example, ice melts at 00 C and water boils at 1000 C, at low temperature the rain drops form in the upper atmosphere. Enzyme beta-galactosidase allows the breaking of the C-O bond that leads to the digestion of lactose .These are complex processes which involve many particles to behave in a collective fashion. This could happen because of the interaction among particles. However, these cannot be solved by Newton’s equations, because we cannot solve Newton’s equations even for three particles interacting system. So the forefathers of this field, Maxwell, Boltzmann and Gibbs introduced probabilistic approach and combined it with mechanics to form the ‘Statistical Mechanics.’ This a branch of theoretical science that parallels Quantum Mechanics and these two together form the main tools at our disposal to understand why things happen and how they happen. The present course will address the basic postulates of Statistical Mechanics and then will show how starting from the basic postulates one builds a formidable framework which can be used to explain phenomena mentioned above.
INTENDED AUDIENCE :Chemistry, Physics, Material Science, Chemical Engineering
PREREQUISITES :Thermodynamics, Basic Algebra and Calculus
INDUSTRIES SUPPORT :Pharmaceutical and fuel cell companies will recognize this course very useful.

COURSE LAYOUT

Week 1: Preliminaries: Objectives of Statistical Mechanics (SM), probability and statisticsWeek 2: Probability and Statistics, Fundamental concepts of SMWeek 3: Phase Space and Trajectories, postulatesWeek 4: Postulates of Statistical Mechanics, Microcanonical ensembleWeek 5: Microcanonical Ensemble, Canonical EnsemblesWeek 6: Canonical Ensemble, Grand Canonical Ensemble, isothermal-isobaric ensembleWeek 7: Fluctuation and Response Functions, ideal monatomic gasWeek 8: Ideal Monatomic Gas: Microscopic Expression of Translational Entropy, ideal gas of diatomic moleculesWeek 9: Ideal Gas of Diatomic molecules: Microscopic Expression of Rotational and Vibrational Entropy and Specific HeatWeek 10:Non-ideal gas, Cluster Expansion and Mayer’s Theory Week 11:Mayer’s Theory for Interacting Systems: Phase TransitionWeek 12:Landau Theory of Phase Transitions: Order Parameter Expansion and Free Energy Diagrams, Nucleation.