Statistical Mechanics

Oberlin College Physics 410

Syllabus for Spring 2019

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 (2:30 pm to 9:00 pm only).

Dan Styer's schedule grid (PDF).

Meeting times: Class: MWF at 11:00 am in Wright Laboratory room 114.
Conference: Wednesday at 9:30 am and Thursday at 10:00 am in Wright Laboratory Seminar Room.

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 1 March at 11:00 am), one in-semester oral exam (on the week starting Monday 8 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 will contribute 25% 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 problem sets rather than from readings.

Problem sets will be distributed on each Friday, except for the Friday preceding the exams. Each is due in class the following Friday; late papers will be accepted only in cases of illness. When writing your solutions, 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 Monday). Your work on the problem sets will contribute 25% to your final grade.

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

Collaboration and references: I encourage you to collaborate or to seek printed help in working the 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]

R. Baierlein, Thermal Physics (Cambridge University Press, 1999). Another impressive textbook. [QC311.B293 1999]

F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill, 1965). Excellent problems, obsolete applications, a shaky grasp of the fundamentals. Sometimes long winded. Good but outdated choice of topics. This is the book I used as an undergraduate. [530.13.R272F]

Charles Kittel and Herbert Kroemer, Thermal Physics, 2nd edition (W. H. Freeman and Company, 1980). Probably the most widely used of the books. [QC311.5.K52 1980]

F.W. Sears and G.L. Salinger, Thermodynamics, the Kinetic Theory of Gases, and Statistical Mechanics, 3rd edition (Addison-Wesley, 1975). Very clear, but rather dry and pedantic. Emphasis is on thermodynamics. See the review in Am. J. Phys. 44 (1976) 192-194. [QC311.S42 1975]

W.G.V. Rosser, An Introduction to Statistical Physics (Ellis Horwood Publishers, 1982). This book has gotten good reviews from students in the past, but is now out of print. [QC174.8.R67 1982]

F. Mandl, Statistical Physics (John Wiley, 1971). [QC175.M24]

Ralph Baierlein, Atoms and Information Theory: An Introduction to Statistical Mechanics (Freeman, 1971). An approach to statistical mechanics completely different from the one that I will use. [QC175.B33]

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

Graduate level texts:

David Chandler, Introduction to Modern Statistical Mechanics (Oxford University Press, 1987). I like this one. [QC174.8.C47 1987]

David L. Goodstein, States of Matter. Wonderful to read, lots of interesting applications, but unfortunately above the level of this course. See the review in Am. J. Phys. 44 (1976) 610-611. [QC173.3.G66 1985]

Donald A. McQuarrie, Statistical Mechanics (Harper and Row, 1976). Good book with a chemical perspective. Nice treatments of molecular gases and of correlation functions. [QC174.8.M3]

Colin J. Thompson, Classical Equilibrium Statistical Mechanics (Clarendon Press, 1988). Very clear, terse overview. [QC174.8.T49 1988]

M. Toda, R. Kubo, N. Saito, Statistical Physics I: Equilibrium Statistical Mechanics (Springer-Verlag, 1983). [QC174.8.T613 1983 vol.1]

R. Kubo, Statistical Mechanics (North-Holland, 1965). A collection of excellent problems interspersed with summaries of the theory. [530.13 K951S]

Books on thermodynamics:

E. Fermi, Thermodynamics (Prentice-Hall, 1937, reprinted by Dover). A clear, thoughtful, and thorough treatment of classical thermodynamics. [536.7 F386T]

Herbert B. Callen, Thermodynamics (Wiley, 1960). See review in Am. J. Phys. 55 (1987) 860-861. [536.7 C132T]

Howard Reiss, Methods of Thermodynamics (Blaisdell, 1965). Nice book with a chemical approach. [QC311.R34 1996]

Mark W. Zemansky, Heat and Thermodynamics, 5th edition (McGraw-Hill, 1968). Particularly good in its treatment of non-standard thermodynamic systems, such as stretched rubber bands, surface films and electrochemical cells. [536 Z4H.3]

Books on computer simulation:

Kurt Binder and D.W. Heerman, Monte Carlo Simulation in Statistical Physics (Springer-Verlag, 1988). A good introduction; the best place to start learning about Monte Carlo. See particularly sections 2.1.6 and 2.2.1. [QC174.85.M64B56 1988]

H. Gould and J. Tobochnik, An Introduction to Computer Simulation Methods: Applications to Physical Systems, part II (Addison-Wesley, 1988). Another introduction. Somewhat long winded, as can be guessed from the title. See particularly chapter 16. [QC21.2.G67 1987 vol. 2]

Kurt Binder, ed., Monte Carlo Methods in Statistical Physics, 2nd edition (Springer-Verlag, 1986). Detailed papers. A good place to look for answers to questions raised in the other books. [QC174.85.M64M67 1986]