Physics · Advanced university
Canonical ensembles and partition functions · revision notes
For a system at inverse temperature β=1/(kBT), the canonical probability of a microstate of energy E is exp(−βE)/Z.
Key ideas and conditions
Canonical weights
For a system at inverse temperature β=1/(kBT), the canonical probability of a microstate of energy E is exp(−βE)/Z.
Partition function
Z sums Boltzmann weights over microstates. Degeneracy must be included when summing over distinct energy levels.
Averages
Mean energy is −∂ln Z/∂β when the energy spectrum is independent of β. Thermodynamic identities inherit the ensemble assumptions.
Physical scope
Canonical equilibrium assumes thermal contact with an appropriate reservoir. It is not a universal model for every evolving system.
Explain without looking
- In a nondegenerate two-level model at the infinite-temperature limit, find excited-state probability.
- Explain one distinction between microcanonical and canonical ensembles.
Further reading and review references
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