Page 12 - STATISTICAL MECHANICS: From First Principles to Macroscopic Phenomena
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x Preface
mechanical systems. The derivation of the equilibrium aspects of thermodynamics
is then presented followed by a discussion of the semiclassical limit.
In the second part, I progress through equilibrium applications to successively
more dense states of matter: ideal classical gases, ideal quantum gases, imperfect
classical gases (cluster expansions), classical liquids (including molecular dynam-
ics) and some aspects of solids. A detailed discussion of solids is avoided because,
at many institutions, solid state physics is a separate graduate course. However,
because magnetic models have played such a central role in statistical mechanics,
they are not neglected here. Finally, in this second part, having touched on the
main states of matter, I devote a chapter to phase transitions: thermodynamics,
classification and the renormalization group.
The third part is devoted to dynamics. This consists first of a long chapter on
the derivation of the equations of hydrodynamics. In this chapter, the fluctuation–
dissipation theorem then appears in the form of relations of transport coefficients to
dynamic correlation functions. The second chapter of the last part treats stochastic
models of dynamics and dynamical aspects of critical phenomena.
There are problems in each chapter. Solutions are provided for many of them in
an appendix. Many of the problems require some numerical work. Sample codes
are provided in some of the solutions (in Fortran) but, in most cases, it is advisable
for students to work out their own solutions which means writing their own codes.
Unfortunately, the students I have encountered recently are still often surprised to
be asked to do this but there is really no substitute for it if one wants a thorough
mastery of simulation aspects of the subject.
I have interacted with a great many people and sources during the evolution of this
work. For this reason acknowledging them all is difficult and I apologise in advance
if I overlook someone. My tutelage in statistical mechanics began with a course
by Allan Kaufman in Berkeley in the 1960s. With regard to statistical mechanics I
have profited especially from interactions with Michael Gillan, Gregory Wannier
(some personally but mainly from his book), Mike Thorpe, Aneesur Rahman, Bert
Halperin, Gene Mazenko, Hisao Nakanishi, Nigel Goldenfeld and David Chandler.
Obviously none of these people are responsible for any mistakes you may find, but
they may be given some credit for some of the good stuff. I am also grateful to
the many classes that were subjected to these materials, in rather unpolished form
in the early days, and who taught me a lot. Finally I thank all my Ph.D. students
and postdocs (more than 30 in all) through the years for being good company and
colleagues and for stimulating me in many ways.
J. Woods Halley
Minneapolis
July 2005