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ChE/Ch
164 Introduction to Statistical Thermodynamics
The
principal texts are D.A. McQuarrie, Statistical Mechanics,
Harper & Row, 1976, and D. Chandler, Introduction to Modern
Statistical Mechanics, Oxford, New York, 1987. Portions of
the material to be discussed are treated in these texts, in
the pages cited below after "Ref. I" and "Ref.
II", respectively. McQuarrie's text covers many topics,
apart from those related to the Ising model and some very
modern results. Chandler's excellent text provides much of
this material, and so is a very useful supplement. Several
other books, referred to and used particularly in latter half
of the course, are given at the end of this syllabus. Nonequilibrium
statistical mechanics is treated in Ch 165. Much of the relevant
part for equilibrium statistical mechanics is contained in
McQuarrie’s Statistical Thermodynamics, which is the
first part of his Statistical Mechanics.
1.
Introduction. Aims of statistical mechanics, various ensembles
and thermodynamics, relevant mathematics (probability distributions,
Stirling's approximation, binomial distribution, Lagrange
multipliers, relation between partial derivatives), brief
thermodynamics review. Ref. I, 13-25; Ref. II, Chaps. 1 and
3; F. Chap. 1.
2.
Canonical ensemble. Distribution function (derivation),
evaluation of Lagrange multipliers using second law, expressions
for thermodynamic functions in terms of canonical partition
function, third law and entropy, remark on microcanonical
ensemble, physical meaning of partition function. Ref. I,
35-47; Ref. II, Chap. 3; F, Chap. 1.
3.
Grand canonical ensemble. Distribution function (derivation),
evaluation of Lagrange multipliers, expressions for thermodynamic
functions in terms of grand canonical partition function,
isothermal-isobaric ensemble. Ref. I, 51-57; F, Chap. 1.
4.
Various statistics. Indistinguishability of particles
and Fermi-Dirac, Einstein-Bose and Boltzmann distribution
functions for noninteracting particles obtained via grand
canonical partition function, thermodynamic properties. Ref.
I, 68-76; R, Chap. 9D.
5.
Noninteracting molecules. Relation of canonical partition
function to molecular partition function and thermodynamic
properties, monatomic, diatomic and polyatomic gases, symmetry
of wave functions, ortho-para hydrogen, chemical equilibria,
phase equilibria. Ref. I, 81-89, 91-109, 129-140, 142-157;
Ref. II, Chap. 4; F, Chap. 2.
6.
Independent modes or particles. Fermi-Dirac system (electron
gas), Einstein crystal, Debye crystal, specific heat, free
electron model of metal, photon gas (black body radiation)
(only briefly mentioned). Ref. I, 177-182, 194-206; Ref. II,
Chap. 4; F. Chap. 2.
7.
Classical statistical mechanics. Phase space, classical
partition function, Ref. I, 113-123, 185-189; F, Chap. 3.
8.
Fluctuations in energy (in canonical ensemble), in magnetization
(canonical ensemble), in number of particles (grand canonical
ensemble and, more generally, in other properties ("thermodynamically
conjugate variables"), smallness of fluctuations, and
equivalence of different ensembles. Ref. I, 57-64; Ref. II,
Chap. 3; F, Chap. 1.
9.
Interacting particles. Lattice statistics, Ising model
for spin systems, partition function for one-dimensional system,
broken symmetry, mean field theory, Curie-Weiss law, discontinuities
at the critical point Bragg-Williams approach to "mean
field" theory, adiabatic demagnetization, free energy.
Ref. II, Chap. 5; Re, part of Chap. 9F; Hi, part of Chap.
7; Z, part of Chap. 5; Hu, Chap. 16; P, part of Chap. 11;
PB, part of Chap. 3.
10.
Applications to lattice-like or mean field problems. Regular
solutions, order-disorder in binary alloys, lattice gas, van
der Waals equation, polymer-solvent solutions (Flory-Huggins
model), liquid crystals. See refs. to Sect. 11. Hi II, part
of Chap. 21.
11.
More on Ising model. Correlation length, transfer matrix
method, renormalization group theory and application to Ising
model. TKS, Chaps. 4.4, 4.5; Ma, part of Chap. 17; P, part
of Chap. 12 and 13. H. J. Maris and L. J. Kadanoff, Am. J.
Phys. 46, 652 (1978); TKS, 171-176. (Application of renormalization
group theory to polymers is given in G, Chap. 11).
12.
Interacting particles (imperfect gases). Thermodynamic
perturbation theory, cumulant expansion, Gibbs-Bogoliubov
bound. Ref. I, 302-306; Ref. II, Chap. 5.5; R, pp. 387-389;
AT, pp. 37-41; Z, 220-223; F, Chap. 9.
Other
texts referred to above are H.L. Friedman, A Course in Statistical
Mechanics (Prentice-Hall, 1985) (F); M. Toda, R. Kubo and
N. Saito, Statistical Physics.I. (Springer-Verlag, 1980) (TKS);
L. E. Reichl, A Modern Course in Statistical Physics (U. Texas
Press, 1980) (R); R. Abe and Y. Takahashi, Statistical Mechanics
(U. Tokyo Press, 1975) (AT); T. L. Hill, Statistical Mechanics
(McGraw-Hill,1956) (Hi); J. M. Ziman, Models of Disorder (Cambridge
U.P., 1979) (Z); K. Huang, Statistical Mechanics (Wiley, 1965)
(Hu); M. Plischke and B. Bergersen, Equilibrium Statistical
Mechanics (Prentice-Hall, 1989) (PB); R. K. Pathria, Statistical
Mechanics, 2nd ed., (Butterworth, 1996) (P); T. L. Hill, Introduction
to Statistical Thermodynamics (Addison-Wesley, 1960) (Hi II).
Other useful texts include D.A. McQuarrie, Introduction to
Statistical Thermodynamics (Harper, 1973); N. Davidson, Statistical
Mechanics (McGraw-Hill, 1962); G. S. Rushbrooke, Introduction
to Statistical Mechanics (Oxford U.P., 1951); H. Eyring, D.
Henderson, B. J. Stoner, E.M. Eyring, Statistical Mechanics
and Dynamics (Wiley, 1982), 2nd. ed.; P. de Gennes, Scaling
Concepts in Polymer Physics (Cornell U.P., 1979).
A
topic not covered in the above syllabus is cluster expansions,
used, for example, in treatments of non-ideal gases, electrolyte
solutions, etc. Treatments are given Ref. I, Chap. 12, and
in Friedman, Chaps. 6, 7, and in other books. Monatomic liquids
are treated in Ref. I, Chap. 13.
Texts on Reserve in Millikan, First Floor
McQuarrie, Statistical Mechanics, overnight.
McQuarrie, Statistical Thermodynamics, overnight.
Davidson, Statistical Mechanics, overnight.
Friedman, A Course in Statistical Mechanics, overnight.
Eyring, Statistical Mechanics & Dynamics, 2nd ed., overnight.
Chandler, Introduction to Modern Statistical Mechanics, overnight.
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