Partition Function
The central mathematical function in statistical mechanics that encodes statistical properties of a system in thermodynamic equilibrium.
Governing formula
Z = ∑ exp(-E_i / (kB T)) = ∑ g_i exp(-E_i / (kB T))
SI unit
Dimensionless
In depth
Acts as the sum over Boltzmann state weights. All thermodynamic quantities (internal energy, entropy, pressure, free energy) are calculated by taking derivatives of $ln Z$.
Examples in the real world
Deriving Planck's blackbody radiation law or heat capacities of solids using quantum partition functions.