Lecture

Grand Canonical and Isothermal Ensembles

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In course

MSE-421: Statistical mechanics

This course presents an introduction to statistical mechanics geared towards materials scientists. The concepts of macroscopic thermodynamics will be related to a microscopic picture and a statistical interpretation. Lectures and exercises will be compleme ...

Description

This lecture covers the derivation of the grand canonical ensemble, which describes systems with a fluctuating number of particles and a fixed chemical potential, and the isothermal isobaric ensemble, where temperature and pressure are held constant. The instructor explains the extended Lagrangian used to define these ensembles, the role of Lagrange multipliers in enforcing thermodynamic conditions, and the link between thermodynamic potentials and partition functions. Through detailed derivations, the lecture illustrates how to obtain the probability distributions for these ensembles and how they are related to the Gibbs free energy. The audience is encouraged to engage with the material by attempting derivations independently.

Instructor

Michele Ceriotti

Michele Ceriotti received his Ph.D. in Physics from ETH Zürich in 2010. He spent three years in Oxford as a Junior Research Fellow at Merton College. Since 2013 he leads the laboratory for Computational Science and Modeling in the Institute of Materials at EPFL. His research revolves around the atomic-scale modelling of materials, based on the sampling of quantum and thermal fluctuations and on the use of machine learning to predict and rationalize structure-property relations. He has been awarded the IBM Research Forschungspreis in 2010, the Volker Heine Young Investigator Award in 2013, an ERC Starting Grant in 2016, and the IUPAP C10 Young Scientist Prize in 2018.

Official source

Ontological neighbourhood

Physics

Thermodynamics: Statistical mechanics

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