Role of symmetry and energy in structural phase transitions

Thermodynamic order of the phase transition (Ehrenfest’s classification): 

smallest order of the derivatives of the Gibbs free energy G (with respect to the relevant 
variable, T or p) which are discontinuous across the transition

First-order transitions:  

the first-order derivatives (entropy S and volume V) are discontinuous, leading to enthalpy 
(latent heat) ∆H and volume ∆V jumps

dG = -SdT + Vdp (1)

Second-order transitions:  

the second-order derivatives (heat capacity Cp and compressibility β) are discontinuous, 
whereas the first-order ones are continuous (no heat or volume effects):

∆S = 0, ∆H = 0, ∆V = 0

d2G = - (Cp/T)dT2 -Vβdp2 -VαdTdp (2)

Phase α stable for T < Tc,   phase β stable for T > Tc →

∆G = Gβ -Gα > 0 for T < Tc,   ∆G = Gβ -Gα < 0 for T > Tc ?