The subject of statistical mechanics is part of the core of physics. It is concerned with predicting the bulk properties of macroscopic matter, especially those affected by thermal energy, from microscopic principles. It provides a fundamental explanation of the laws of thermodynamics, including the second law (the tendency of entropy to increase for isolated systems). Statistical physics accounts for the behavior of photons and phonons, explains what happens to ideal gasses in the quantum limit, and accounts for the transformations of matter between different phases. It explains what happens as the absolute zero of temperature is approached, explains the transport of heat and momentum, and provides insight into novel phenomena at the frontiers of physics, including the amazing Bose-Einstein condensation, the behavior of nuclear matter in stars, and other exciting developments involving many particle systems.
The central conceptual ideas in statistical physics include the laws of thermodynamics, especially the second law and the concept of entropy; the canonical probability distribution, which specifies how likely it is that a system at constant temperature will be found in a particular one of its many possible states; the partition function, from which all the thermodynamic properties of a system can be obtained; and the chemical potential, which allows one to understand diffusive equilibrium in a system whose particles can move around.
Students who haven’t experienced the subject often misunderstand what statistical physics is about, thinking from the name that it’s about computing odds for atoms to do different things. However, given the huge number of particles (atoms, photons, electrons, etc.) in a typical macroscopic system, it really provides perfectly definite predictions or explanations of most important properties.
In recent years, statistical physics has undergone an amazing expansion, so that it is now often used outside its traditional domain (thermal properties of matter), e.g. in biological physics, including efforts to understand genetic sequences, and in “financial physics”, to understand stock market fluctuations(!). If you pay attention, you might make a lot of money (or you might not).
Background: The background required for this course is modest. From quantum physics, you need to understand the existence of energy eigenstates and the concept of the de Broglie wavelength. From classical mechanics, you don’t need much more than introductory physics. The ideas of thermodynamics will be taught from scratch in the course. The mathematical level of the course is comparable to sophomore physics, i.e. multivariable calculus, but vector calculations are not usually needed.
The primary required text will be Daniel V. Schroeder, Thermal Physics, a book that has received several outstanding reviews. It emphasizes not only core ideas of the subject, but also wide applicability, including its role in chemistry, atmospheric science, and astrophysics. It offers a wide range of problems, including some based on numerical computation. Previous students have considered this book to be exceptionally good.
There is a useful web site for this text, containing corrections, suggested readings, and a wide variety of relevant URL links: http://departments.weber.edu/physics/thermal/
Other useful texts, on reserve, include:
Ralph Baierlein, Thermal Physics, an excellent recent text by a distinguished emeritus faculty member from Wesleyan University. This would have been a possible text for the course, and I recommend it highly to provide a different point of view.
F. Reif, Statistical Physics. Older but excellent.
Kroemer and Kittel, Thermal Physics. A bit terse, but worth consulting.
J.S. Dugdale, Entropy and its Physical Meaning
M. Glazer and J. Wark, Statistical Mechanics: A Survival Guide
I like classroom interaction and believe it is important for your learning. To ensure that there is substantial interaction, and to make sure that the problem sets are integrated with the course, there is a required weekly tutorial (most weeks). Occasionally, a lecture and tutorial may be interchanged.
Regular attendance: You are expected to attend all classes and tutorials. Absences for any reason other than illness, family situation, or job interview will be considered excessive if more than two in number at class or tutorial. If you are ill or expect to miss class due to special circumstances, a timely e-mail message to that effect is expected. Especially in a small course, each person counts.
Preparation: You should come to class prepared. The best learning occurs when you read or skim the upcoming material before class, and then read more carefully after class. Interaction during lectures is expected and encouraged.
Homework: There will be regular homework assignments. You are expected to complete the homework (or at least to make a serious effort on each problem) on time. Some problems will be designated as "individual" problems, for which you may not consult with classmates, but may use the library. You should not expect to be able to do all of the problems successfully.
Tutorials: These sessions will be devoted to discussing homework, both to provide assistance, and to give you practice in oral presentation. The class will be divided into working groups. Each week, two problem will be assigned to each problem-solving group for presentation. The groups meet in advance of the tutorial to confer, and one or more members of the appropriate groups will present the problem. Presentation is expected to rotate so that over time, everyone presents equally often. Note that there isn’t time to present solutions in detail. Rather a sketch or list of key issues should be given, with advice, partial answers, and pitfalls to avoid. You can then respond to questions.
The group as a whole is evaluated for its efforts in preparing for tutorial. Everyone can earn high esteem from the instructor and classmates by contributing generously to the discussion, volunteering ideas, and also by posing questions when you’re mystified. We must all strive for a collegial atmosphere in which corrections are proffered gently and accepted graciously without embarrassment. Attendance is mandatory, and it is expected that you will have worked on each problem (not necessarily successfully) in advance. I recognize that you will work harder before tutorial on the problems for which your group is responsible, but in preparing your final solutions, you will make up for this.
Exams: There will be two take-home exams, of which one is at the end of the semester. Each will be 2-3 hours in duration, and will be “closed book” except for a page of notes.
Computer project: There will be a computer project (on the famous Ising model) toward the end of the course.
Grading philosophy: When evaluating students’ work, I look for effort, engagement, and mastery on an individual basis. The performance of one student does not affect the grades received by others. Historically, the average grade of students in upper level courses I have taught is around 3.3 (B+ on a letter grade scale), but each class is different.
Weights: The following weights will be applied to the various components.
Exams (2) 25%, 25%
Computer project: Ising Model 10%
Homework: I will read the "individual" problems and check a subset of the others. I will not be able to read all of the homework. Please note that clarity and the use of explanatory prose is expected.
Late assignments: Homework is generally due at the class following tutorial. Homework turned in up to one week late will receive 75% of the earned grade. (Solutions are posted on that day.) Beyond that, you may obtain up to 50% credit, and it is permissible in this case to refer to the posted solutions for ideas, but not to copy the solutions. Additional exception: you may have a "free extension" for up to one week without penalty once in the term. Please save it for a high pressure time. Simply turn in a sheet of paper with your name, the assignment number, and the remark that you are taking the "free extension."
Unexcused absences will be considered in the final evaluation if more than two were noted.
You are allowed and encouraged to discuss homework with each other (except on "individual" problems), but it would be wise to attempt them yourself first. Your written work must be your own, though it may be influenced by prior discussion. This means, for example, that you may not look at another student’s written work while preparing your own. Two assignments that have substantially identical wording or equations in one paragraph or more would be presumed in violation of the honor code.
Sources (e.g. books) or other assistance should be acknowledged. However, you don't need to acknowledge the help of students in your problem-solving group since this interaction is understood.
Similar expectations apply to the computer project: You may and should help each other, but you must keep your own computer files, make and annotate your own printouts, and do your own accompanying written work.
The purpose of these provisions is to enhance your learning experience, and to enable the instructor to tell how well each student is doing.
Electronic mail (sent to jgollub) is always welcome and will generally be answered between 2 and 6 p.m. on weekdays and often on Sunday afternoon or evening.
Phone: You may phone my office at 896-1196. Please leave a message if I'm not there, along with a suggested time in the evening when I can return your call. It’s OK to call me at home (649-4159) from 9 to 11 p.m. occasionally, Sunday through Thursday.
Office: I will be very happy to speak with you immediately after any class period (at 10:30 a.m.) , or to arrange an appointment at a mutually agreeable time. Please also do not feel shy about dropping in or about phoning. If busy, I'll suggest another time.
I look forward to working with you. I appreciate your feedback, and urge you to communicate any concerns without delay.
In general we will follow the sequence of the text, but will skip sections 5.4-5.5, and 8.1. It is a bit hard for me to tell you now the timing for the entire course, because I want to feel free to adapt the time spent on each topic based on my perceptions of your progress.