# Mathematical properties of free Gibbs energy

I'm wandering, if some mathematical properties of the free Gibbs energy (also called thermodynamic potential) are well known. For instance in chemistry, if $n_i^\alpha$ denotes the number of moles of species $i$ in phase $\alpha$ and G is the free Gibbs energy. I know that G must be an homogeneous function of degree one in $n_i^\alpha$.

Do we have more information like continuity or coercivity properties of G ?