Z = Σ_i e^(−β E_i) where β = 1/(k_B T). All equilibrium thermodynamic quantities follow by differentiation of ln Z.
Partition function
Related concepts
- Boltzmann constant (k_B)
- e (Euler's number)
- Maxwell-Boltzmann distribution
- Fermi-Dirac distribution
- Bose-Einstein distribution
- Equipartition theorem
- Fluctuation-dissipation theorem
- Maxwell-Boltzmann distribution
- Boltzmann entropy formula
- Helmholtz free energy F
- Canonical ensemble
- Generating function
- Polymer statistical mechanics
- Kramers' rate theory
- Arrhenius 1889: k(T) = A·exp(−E_a/(k_B T))
- Equipartition: ⟨(1/2) k T⟩ per classical quadratic DoF; γ = 1 + 2/f
- QHO partition function: Z = 1/(2 sinh(β ℏω/2)) per normal mode
- Equipartition: monatomic ⟨U⟩/NkT = 3/2, C_V/Nk = 3/2, γ = 5/3; diatomic γ = 7/5
- QHO Z = 1/(2 sinh(βℏω/2)) ≡ exp/geom form; βℏω=log 4 ⇒ Z = 2/3