What is partition function ?

The partition function is a fundamental quantity in statistical mechanics that describes how a system is distributed among its possible energy states.

For a system in thermal equilibrium:

Z = Σ e⁻ᴱⁱ/ᵏᴮᵀ

where Eᵢ is the energy of the ith state, kB is the Boltzmann constant, and T is the absolute temperature.

The partition function is useful because many thermodynamic quantities, such as internal energy, entropy, and Helmholtz free energy, can be calculated from it.