Statistical Mechanics

Oberlin College Physics 410

Syllabus for Spring 2024

Learning goals: Through your work in this course, you will

Aldo Leopold wrote "We speak glibly of ... education, but what do we mean by it? If we mean indoctrination, then let us be reminded that it is just as easy to indoctrinate with fallacies as with facts. If we mean to teach the capacity for independent judgment, then I am appalled by the magnitude of the task." The ultimate goal of this course (and, I hope, of all your other courses) is to develop your capacity for thoughtful, informed, independent judgment.

Teacher: Dan Styer, Wright 215, 440-775-8183, Dan.Styer@oberlin.edu
home telephone 440-281-1348 (9:00 am to 8:00 pm only).

Dan Styer's schedule grid (PDF).

Pronouns, nouns, adjectives, and the character of science: I don't care what pronouns you use when referring to me. Similarly, you may call me "Dan", or "Mr. Styer", or "Dr. Styer", or "Prof. Styer", whichever you find most comfortable. My personal preference, however, is that you call me "Dan". In this course I will present upsetting conclusions violently opposed to our common sense and common experience. (For example: That a gas of non-interacting fermions is hard despite the lack of repulsion. I make no apologies for presenting upsetting conclusions: An education that avoids difficult or disturbing issues is no education at all.) I hope you'll accept those conclusions because they are based on experimental evidence and on cogent, clear, fact-based reasoning -- experiments and reasoning that you or I or anyone else could execute. If you accept those conclusions instead because I have earned the right to put a fancy shingle in front of my name, my teaching will have been an abject failure.

Meeting times: Class: MWF at 11:00 am in Wright Laboratory room 114.
Conference: Wednesday at 1:30 pm in Wright Laboratory room 114.

Course web site: http://www.oberlin.edu/physics/dstyer/StatMech. I will post handouts, problem assignments, and model solutions here.

Textbooks:

The problem assignments will come from my draft book rather than from Schroeder, but the text I've written so far is often quite sketchy.

Exams, homework, grading: There will be one in-semester written exam (due Friday, 8 March at 11:00 am), one in-semester oral exam (on the week ending Friday, 19 April), and a written final (due Thursday 16 May at 9:00 pm). Each written exam will be a two-hour open-book take-home exam. The oral exam will be a conversation, about half an hour long, in my office. Each of the three exams contributes 20% to your final grade. I am using an oral exam because: (1) Physics involves both formal and informal reasoning, but written exams usually test only the formal side. (2) It will be good practice for oral exams that you might face in the future, such as honors exams or graduate qualifying exams. Both types of exams will cover topics from lectures and assignments rather than from readings.

Problem assignments will be distributed on each Wednesday, except for the Wednesday preceding the exams. Each is due in class the following Wednesday; late papers will be accepted only in cases of illness or family emergency. In writing your solutions, do not just write down the final answer. Show your reasoning and your intermediate steps. Describe (in words) the thought that went into your work as well as describing (in equations) the mathematical manipulations involved. I will not grade your homeworks in detail. Instead I will distribute detailed solutions to the assigned problems, and I will skim your solutions very lightly (attempting to get them back to you on Friday). Your work on the assignments contributes 40% to your final grade.

Anyone earning a final score of 50% or lower will not receive credit for this course.

Collaboration and references: You are welcome to consult the library, the Internet, AI resources such as ChatGPT, your friends, or your enemies in working the assigned problems, but the final write-up must be entirely your own: you may not copy word for word or equation for equation. When you do obtain outside help you must acknowledge it. (E.g. "By integrating Schroeder equation (6.62) I find that..." or "Employing the substitution u = sin(x) (suggested by Carol Hall)..." or even "In working these problems I benefited from discussions with Mike Fisher and Jim Newton.") Such an acknowledgement will never lower your grade; it is required as a simple matter of intellectual fairness.

Topics:

  1. The properties of matter in bulk. What is statistical mechanics about? Fluid statics. Descriptive phase diagrams.
  2. Principles of statistical mechanics. Probability, random numbers, games of chance. The microcanonical ensemble. What is entropy?
  3. Thermodynamics. Basics. Heat and work. Multivariate calculus. Applications to fluids, to phase transitions, to chemical reactions, and to light.
  4. Ensembles. More principles of statistical mechanics. Canonical, grand canonical, and other ensembles. Temperature and chemical potential as control parameters.
  5. Classical ideal gases.
  6. Quantal ideal gases. Fermi-Dirac and Bose-Einstein statistics.
  7. Harmonic lattice vibrations. Phonons.
  8. Weakly interacting fluids. Perturbation theory, variational methods. Correlation functions.
  9. Strongly interacting systems and phase transitions. Magnetic systems. Mean field approximation, transfer matrices, computer simulations. Polymers, antiferromagnets, path integrals...the sky's the limit!

Statistical Mechanics Bibliography

The following books are on reserve in the Science Center Library. (They are located on shelves on the west wall, on the left beyond the circulation desk, near some comfy chairs to encourage browsing.)

Popular works:

P.W. Atkins, The Second Law (Freeman, 1984). [QC311.5.A8 1984]

Undergraduate level texts:

D.V. Schroeder, An Introduction to Thermal Physics (Addison-Wesley, 2000). For sale at the campus bookstore as a text. [QC311.15.S32 2000]

Neil Gershenfeld, The Physics of Information Technology (Cambridge, 2000). Entropy related to information. [TK5103.G45 2000]