MSE-421: Statistical mechanics

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Lectures in this course (26)

Covers the fundamentals of classical thermodynamics, from classical mechanics to statistical mechanics, and key thermodynamic variables.

Classical Thermodynamics: Fundamentals and Principles

Covers classical thermodynamics fundamentals, including boundary conditions, internal energy, entropy, and equilibrium principles.

Thermodynamic Principles: Equilibrium, Constraints, and Potentials

Explores internal constraints, equilibrium, variational principles, thermodynamic potentials, and Maxwell relations in classical thermodynamics.

Classical Thermodynamics: Fundamentals and Equilibrium Conditions

Covers the fundamentals of classical thermodynamics, including heat capacity definitions, equilibrium conditions, and phase transitions.

Probability and Measure: Fundamentals and Applications

Covers fundamental concepts of probability theory and measure theory, including joint probabilities, random variables, and the central limit theorem.

Statistical Definition of Entropy: Microstates and Macrostates

Covers microstates, macrostates, entropy, and density of states in statistical mechanics.

Statistical Definition of Entropy: Adatoms and Mixing

Explores the statistical definition of entropy, adatoms on a surface, and mixing in a solid solution.

Canonical Ensemble: Partition Function and Ideal Gas

Explores the canonical ensemble, partition function, and ideal gas properties.

Paramagnetism: Microcanonical vs Canonical Treatment

Delves into the microcanonical and canonical treatment of paramagnetism in external fields.

Gibbs Entropy and Information Theory

Explores Gibbs's entropy, information theory, and the information content of events in non-equiprobable scenarios.

Canonical Distribution: Gibbs Entropy and Ensembles

Explores the derivation of the canonical distribution based on Gibbs's entropy and a maximum entropy principle.

Grand Canonical and Isothermal Ensembles

Explores the grand canonical and isothermal isobaric ensembles and their thermodynamic implications.

Gibbs Entropy and more Ensembles: Uncorrelated Fluctuations and Ideal Gas Law

Explores uncorrelated fluctuations, the ideal gas law, and the Langmuir adsorption isotherm.

Indistinguishable Particles in Quantum Mechanics

Explores indistinguishable particles in quantum mechanics, discussing symmetry, density matrix, quantum statistics, exclusion principle, and particle behavior.

Bose-Einstein Statistics: Derivation and Applications

Explores the derivation and application of Fermi and Bose statistics in different ensembles.

Vibrations in Solids: Harmonic Oscillators and Phonons

Explores vibrations in solids, including harmonic oscillators, phonons, and the Einstein model of heat capacity.

Vibrations and Electronic Excitations

Explores phonon frequencies, heat capacity, thermal properties, vibrations in solids, free electron gas, Fermi function, and density functional theory.

Ferromagnets and the Ising Model

Covers the Ising model, ferromagnetic materials, spins on a lattice, and spin correlations.

Phase Transitions in the Ising Model

Explores phase transitions in the Ising model, mean magnetization, susceptibility, critical exponents, and the universality of critical exponents.

Atomistic Computer Modelling of Materials: Simulating and Sampling

Covers simulating and sampling in atomistic computer modelling of materials.

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