In addition to things like phase transitions, Bose-Einstein condensation etc, an interesting aspect of stat mech is that it works, yet isn't fundamental.
Since it isn't fundamental, how can it be derived?
The overlap of QM, gravity, and thermo/stat mech is very interesting. Quantum black holes have a temperature. Do they obey stat mech? If so, what are the quantum states to be counted, especially since classically black holes have "no hair"?
Incidentally, the theory of critical phenomena in classical stat mech is how the meaning of quantum field theory was understood, and people (who were not rigourous mathematicians) stopped worrying that renormalization was this bizarre process of subtracting infinities, because the stat mech picture provided a good physical picture of renormalization.
Also, don't forget that the dawn of the quantum age started with Planck's derivation of the black body formula using stat mech!
WannabeNewton said:
TomServo said:
And WannabeNewton, why do you like that book?
The lecture notes from which the book was made are available free at
http://ocw.mit.edu/courses/physics/...chanics-of-particles-fall-2007/lecture-notes/. The notes for the second part of the course which covers critical phenomena are at
http://ocw.mit.edu/courses/physics/...-physics-of-fields-spring-2008/lecture-notes/.
I too like Kardar's books very much. Some books like Reif place stat mech above classical thermodynamics, but Kardar presents succintly all of classical equilibrium thermodynamics first. A wonderful thing is his presentation of Clausius's derivation of entropy as a state function, and the second law of thermodynamics from simple English statements (the Kelvin and Clausius statements). I think Clausius's discovery is as beautiful as Einstein's derivation of the Lorentz transformations from the Principle of Relativity and a speed of light that is the same in all inertial frames. Kardar doesn't hesitate to briefly discuss "philosophical" questions like the origin of irreversibility, one ingredient of which is a large number of particles. Kardar is also careful to note interesting details like the differences between the microcanonical and canonical ensembles (p87 of the first set of notes).
Another very good book, but less philosophical is Peliti's "Statistical Mechanics in a Nutshell". For introductory thermo, I like Adkins's "Equilibrium thermodynamics".