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This the course page for Statistical Mechanics and Chemistry, taught by Prof. Pratyush Tiwary in Spring 2025. Relevant links, references etc. will be uploaded here. I will also upload homework/exam problems here (but likely not their solutions except those for midterms and final exam). The class will taught in-person, with recorded videos through youtube available after class. However you should try your best to attend the live classes and engage in discussions on the slack workspace if you want to make the best of this class.
What's new:
What's new:
Midterm 2 details are available via slack
Homework 5 (PDF file) is now available. This is the last homework for the semester.
Final exam (in-class, no internet/notes access, 2 page cheat sheet allowed) will be held as per University timetable on May 15, Thursday, 10:30 AM - 12:30 PM in CHM 1224 (your regular classroom). Details will be discussed in class before the exam.
Lectures:
Lectures:
Lectures 23, 24, 25 (5/6a, 5/6b, 5/8): Midterm 2 presentations, broken symmetry, correlation length, susceptibility. Introduction to Renormalization Group, wrap-up.
Lecture 25 PDF notes, video (youtube link)
Lecture 24 PDF notes, video (youtube link)
Lecture 23 PDF notes, video (youtube link)
Lectures 21, 22 (4/29, 5/1): Ising Models and Peierls droplet argument to phase transitions in 1-d and 2-d Ising model. Mean field theory for phase transitions.
Lecture 22 PDF notes, video (youtube link)
Lecture 21 PDF notes, video (youtube link)
Extra notes on Pierels Droplet argument (PDF file)
Lecture 20 (4/24): Van der Waals equation of state from perturbation theory. [What's next: Ising Models and Peierls droplet argument to phase transitions in 1-d and 2-d Ising model. Mean field theory for phase transitions. Broken symmetry, correlation length, susceptibility. Introduction to Renormalization Group, wrap-up.]
Lecture 20 PDF notes, video (youtube link)
Lectures 18, 19 (4/15, 4/17): Potential of mean force. Equation of state for interacting systems. Zwanzig's statistical mechanics perturbation theory. [What's next: Van der Waals equation of state from perturbation theory. Ising Models and Peierls droplet argument to phase transitions in 1-d and 2-d Ising model. Mean field theory for phase transitions. Broken symmetry, correlation length, susceptibility. Introduction to Renormalization Group, wrap-up.]
Lecture 19 PDF notes, video (youtube link)
Lecture 18 PDF notes, video (youtube link)
Extra reading: Henderson theorem (PDF)
https://drive.google.com/file/d/1Vqbfe69CQ7NF0UCaGMXPB81080kAILkW/view?usp=sharing
Lectures 16, 17 (4/8, 4/10): Interacting systems/classical fluids. Distribution functions.
Lecture 17 PDF notes, video (youtube link)
Lecture 16 PDF notes, video (youtube link)
Lecture 15 (4/1): Classical limits for quantum ideal gases. Free electron model for metals.
Lecture 15 PDF notes, video (youtube link)
Homework 3+4 (double homework, PDF file).
Lectures 13, 14 (3/25, 3/27): Blackbody radiation and Planck distribution. Ideal gas of quantum particles: Fermi-Dirac and Bose-Einstein statistics. Classical limits for quantum ideal gases. [What's next: Free electron model for metals...]
Lecture 14 PDF notes, video (youtube link)
Lecture 13 PDF notes, video (youtube link)
Read: Extra notes on blackbody radiation (PDF)
Lecture 12 (3/11): Einstein and Debye Models for heat capacity of phonons.
Lecture 12 PDF notes, video (youtube link)
Lectures 10-11 (3/4, 3/6): Non-interacting ideal systems. Phonon gas: Inability of classical mechanics to explain heat capacity measurements, quantum statistical mechanics to the rescue.
Lecture 11 PDF notes, video (youtube link)
Lecture 10 PDF notes, video (youtube link)
https://www.youtube.com/watch?v=XH0SAlrFNDY
Lectures 8-9 (2/25, 2/27): Grand canonical ensemble and grand potential. Number fluctuations. Gibbs entropy.
Lecture 9 PDF notes, video (youtube link)
Lecture 8 PDF notes, video (youtube link)
Lectures 6-7 (2/18, 2/20): Fluctuations in canonical ensemble. Thermodynamics from canonical ensemble. Example using microcanonical and canonical ensembles.
Lecture 7 PDF notes, video (youtube link)
Lecture 6 PDF notes, video (youtube link)
Lectures 4-5 (2/11, 2/13): Thermodynamics from microcanonical ensemble. Why does not the energy "shell width" matter in microcanonical ensemble. Canonical ensemble. Fluctuations in canonical ensemble. Thermodynamics from canonical ensemble.
Additional optional reading: Surprises in high dimension (PDF)
Lecture 5 PDF notes, video (youtube link)
Lecture 4 PDF notes, video (youtube link)
Lecture 3 (2/4): Introduction to ergodic hypothesis and ensembles. Microcanonical ensemble and the principle of equal a priori probabilities.
Watch: This Youtube video (at least the first lecture by Susskind)
Lecture 3 PDF notes, video (youtube link)
Lectures 1-2 (1/28, 1/30): An ode to Thermodynamics but why we need Statistical Mechanics. Math and Thermo refresher. Introduction to ergodic hypothesis and ensembles.
Watch: This Youtube clip (7 min 33 sec)
Lecture 2 PDF notes, video (youtube link)
Lecture 1 PDF notes, video (youtube link)
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