Field of Science

Tolman, “The Principles of Statistical Mechanics, Chapter 1, Part 1

Survey of classical mechanics: Generalized coordinates and momenta. Lagrangian equations. Derivation of Hamilton’s equations from Lagrangian. Poisson brackets. Hamilton as representing invariant E under time for conservative systems.

“Pull quote”: Something simple and seemingly obvious but actually deep and foundational

Some notes (not checked for typos!)


  1. "the average behavior ... suitably chosen ... may be much easier to treat ...". Without the "suitably chosen", is this more than a first order mean field approximation, which will not be empirically adequate in the typically more interesting physical cases when higher-order approximations come into play?
    The "suitably chosen" seems to me to raise the game enormously, because if we get the "suitably" right, that becomes in itself a higher-order approximation. But now I have two questions about your reading of how Tolman presents how we can create or find a good suitable choice: how ad-hoc are his suggestions? Is there any kind of choice that he proscribes, and for what reason?
    Whether you feel that these are worth answering or not —now or later, as you read more— in any case I love that this is from 1938. I can see why you've chosen this as a good historical starting point and I look forward to what else you will have to say as your reading progresses.

  2. Good question. In the second chapter he tackles “suitable” head on when he starts talking about ensembles. Will find out soon enough.


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