In thermodynamics, the entropy of fusion is the increase in entropy when melting a solid substance. This is almost always positive since the degree of disorder increases in the transition from an organized crystalline solid to the disorganized structure of a liquid; the only known exception is helium. It is denoted as Δ S fus {\displaystyle \Delta S_{\text{fus}}} and normally expressed in joules per mole-kelvin, J/(mol·K).

A natural process such as a phase transition will occur when the associated change in the Gibbs free energy is negative.

Δ G fus = Δ H fus − T × Δ S fus < 0 , {\displaystyle \Delta G_{\text{fus}}=\Delta H_{\text{fus}}-T\times \Delta S_{\text{fus}}<0,}

where ⁠ Δ H fus {\displaystyle \Delta H_{\text{fus}}} ⁠ is the enthalpy of fusion. Since this is a thermodynamic equation, the symbol ⁠ T {\displaystyle T} ⁠ refers to the absolute thermodynamic temperature, measured in kelvins (K).

Equilibrium occurs when the temperature is equal to the melting point T = T f {\displaystyle T=T_{f}} so that

Δ G fus = Δ H fus − T f × Δ S fus = 0 , {\displaystyle \Delta G_{\text{fus}}=\Delta H_{\text{fus}}-T_{f}\times \Delta S_{\text{fus}}=0,}

and the entropy of fusion is the heat of fusion divided by the melting point:

Δ S fus = Δ H fus T f {\displaystyle \Delta S_{\text{fus}}={\frac {\Delta H_{\text{fus}}}{T_{f}}}}