Statistical Mechanics (mostly equilibrium)

Statistical Mechanics – MEGR 7090/8090

Lecture Notes

1) Introduction; overview of macroscopic equilibrium thermo: lecture1-macrothermo-review 

2) Derivation of Gibb’s relations, Maxwell relations, generalized du:  lecture1-notes

3) More macroscopic thermo:  lect2-macro-review-cont

4) Fundamental postulates, part 1: lecture2-part2-notes

5) Fundamental postulates, part 2: lecture2-aside-estimate-probability-1-ptcl-total-energy-5

6) Fundamental postulates, part 3:  lecture3-generallization-fund-postulates-n-indep-particle-systems-6

7) Boltzmann’s attempt to connect micro- and macroscale equilibrium thermo:  lecture2-part1-notes-7 

8) Derivation of Boltzmann entropy relation (ca 2015): lec4-derivation-boltzmann-relation-8

9) Relation between k and universal gas constant; rough repeat of Reif’s degree-of-freedom argument: lec4-2015-connectktor-9

10) Rough rederivation of Reif’s DoF argument; rough alternate derivation of number of quantum states in an N-particle ideal gas: lec4-rough-2015-reifdofpluspathrianoofstatesigas-11


11) Quantum mechanics overview, part 1: lecture-4-quantum-mech-overview-part1-12

 12) Quantum mechanics overview, part 2 (rough): lecture-4-quantum-mech-overview-rough-version-part1-13

 13) Ensemble overview; QM recipe; when to choose quantum versus classical model: ensemble-method-overview-quantum-mech-recipe-thermal-wavelength-2015-14

14) Derivation of canonical distribution: canonical-distbn-derivation-2015-16

15)  Rederivation of canonical distribution; overview of phase space of N-particle system:   lec9-2015-phase-space-deriavtion1-canonical-density-fn-17

16) Improved derivation of canonical distribution: canon-distbn-good-dervn-version1-2015-18

17) Derivation of A=kTlnQ; G=μN; S=k ∑ plnp; S = k ln Ω: dervnaktlnq-gmun-sksumprlnpr-20

18) Degenerate states; example degeneracy estimate for single particle in aa box (not  in Pathria): dervn-canon-dist-degenerate-energy-levels-22

19) Rigorous derivation of microcanonical distribution (not in Pathria): rigorous-dervn-microcanonical-distribution-22

20) On the equivalence of state density, g(E), and Ω:  eqivalence-of-ge-omega-23

19) Rigorous derivation of microcanonical distribution (not in Pathria): rigorous-dervn-microcanonical-distribution-22

20) Example calculation of g(E) for classical ideal gas (Laplace transform inversion):  laplace-inversion-ex-ge-aside-quantum-conversion-factor-24

21) Example calculation of partition function, Q, for classical ideal gas:  example-calc-partition-fn-classical-ideal-gas-25

22) Derivation of Liouville theorem: dervn-continuum-cons-eqns-via-kirkwood-liouville-theorem-26

23) Interacting particle systems; molecular-scale conservation laws: interacting-classical-particle-systems-molecular-scale-conservation-laws-part1-27

24) Molecular-scale ensemble-averaged momentum equation: derivn-ensemble-avg-molecular-scale-momentum-eqn-28

25) Appendix 1: Quantum energy states of a free particle in a box: lecture-5-quantum-energy-lstates-free-ptcl-29

26) Appendix 2: Details underlying Pathria’s derivation of quantum phase space volume: lecture-11-dervn-of-no-quantum-states-per-unit-vol-phase-space-30

27) Appendix 3: Combinatorics warm-up:  combinatorics-1-lec5-2015-31

28) Appendix 4: X and P bases in quantum mechanics: lecture-18-pt1-x-and-p-bases-in-qm-32


Send email to