Configurational entropy ($S_{\mathrm{conf}}=k_B\ln {\Omega }_{\mathrm{conf}}$)

The part of entropy associated with the number of distinct spatial or occupancy arrangements consistent with chosen macroscopic constraints. For equally weighted configurations, the Boltzmann entropy formula gives the displayed expression. Unequal probabilities require $-k_B{\sum }_i{p}_i\ln p_i$ over configurations. For $n$ indistinguishable empty sites among $M$ otherwise occupied sites, ${\Omega }_{\mathrm{conf}}=\left(\genfrac{}{}{0ex}{}{M}{n}\right)$. Vibrational or internal degrees of freedom can contribute additional entropy even at fixed site arrangement.

Randomly distributing $n$ species with equal fractions over $N$ sites gives $\Omega =N!/[(N/n)!{]}^n$. Stirling approximation gives $S=k_{B}N\ln n$, or $R\ln n$ per mole of sites. Configurational entropy alone does not decide whether a multicomponent alloy is a stable single thermodynamic phase.