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.^[1] It is denoted as ${\displaystyle \Delta S_{\text{fus))}$ 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.

${\displaystyle \Delta G_{\text{fus))=\Delta H_{\text{fus))-T\times \Delta S_{\text{fus))<0,}$

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

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

${\displaystyle \Delta G_{\text{fus))=\Delta H_{\text{fus))-T_{f}\times \Delta S_{\text{fus))=0,}$

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

${\displaystyle \Delta S_{\text{fus))={\frac {\Delta H_{\text{fus))}{T_{f))))$

Helium

Helium-3 has a negative entropy of fusion at temperatures below 0.3 K. Helium-4 also has a very slightly negative entropy of fusion below 0.8 K. This means that, at appropriate constant pressures, these substances freeze with the addition of heat.^[2]