Sethna P. Statistical mechanics.. Entropy, Order parameters plexity (book draft, CUP, 2005)(298s)_PT_.pdf

Statistical Mechanics:
Entropy, Order Parameters
plexity
James P. Sethna, Physics, Cornell University, Ithaca, NY
∞ c April 19, 2005
B
Q b
F
x
SYSTEM
Alcohol
E
Two-Phase Mix
E+ 1 E Water Oil
Electronic version of text available at
.edu/sethna/StatMech/
Contents
1 Why Study Statistical Mechanics? 3
Exercises.............................. 7
QuantumDice..................... 7
Probability Distributions. . . . . . . . . . . . . . . 8
Waitingtimes..................... 8
Stirling’s Approximation and Asymptotic Series. . 9
RandomMatrixTheory................ 10
2 Random Walks and Emergent Properties 13
Random Walk Examples: Universality and Scale Invariance 13
................... 17
................. 19
............... 21
Fourier........................ 21
Green......................... 22
Exercises.............................. 23
Random walks in Grade Space. . . . . . . . . . . . 24
Photon diffusion in the Sun. . . . . . . . . . . . . . 24
Ratchet and Molecular Motors. . . . . . . . . . . . 24
Solving Di1usion: Fourier and Green. . . . . . . . 26
Solving the Di1usion Equation. . . . . . . . . . . . 26
FryingPan...................... 26
ThermalDi1usion................... 27
PolymersandRandomWalks............ 27
3 Temperature and Equilibrium 29
The Microcanonical Ensemble . . . . . . . . . . . . . . . . 29
The Microcanonical Ideal Gas . . . . . . . . . . . . . . . . 31
Configuration Space . . . . . . . . . . . . . . . . . 32
MomentumSpace.................. 33
?.................... 37
Pressure and Chemical Potential . . . . . . . . . . . . . . 40
Entropy, the Ideal Gas, and Phase Space Refinements . . 44
Exercises.............................. 46
EscapeVelocity.................... 47