1. Lecture 3: Other Ensembles and
Statistical Thermodynamics
Lecture 3: Other Ensembles and
Fluctuations
Dr. Ronald M. Levy

2. Thermodynamic connection
Other ensembles
Partition function
Thermodynamic connection
(1)
(2)
(3)
Gibbs free energy
(4)
(5)
(6) 1

3. Equivalent information
Microcanonical entropy
canonical entropy
(7)
(8)
states
energy
(9)
Rapidly increasing function of E
Rapidly decreasing function of E
Sharply peaked function 2

4. Equivalent information
(10)
(11)
(12)
(13)
(14) 3

5. Energy fluctuation in canonical ensemble and CV4

6. Energy fluctuation in canonical ensemble and CV
(14)
(15)
(16) 5

7. (17)
(18)
(19) 6

8. Canonical distribution
(20)
(21) 7

9. Canonical distribution
(22)
(23)
(24) 8

10. Canonical distribution
In general, a canonical ensemble is a distribution over microcanonical ensembles, it “degenerates” to microcanonical ensemble.
In the microcanonical ensemble, the energy of the system is fixed, there are no energy fluctuation.
In canonical ensemble, only the average energy is fixed. 9

11. Grand canonical partition function
(25)
N: # molecules
j: states
(26)
(27) 10