As the internal energy is a convex function of entropy and volume, the stability condition requires that the second derivative of internal energy with entropy or volume to be positive. It is commonly expressed as . Since the maximum principle of entropy is equivalent to minimum principle of internal energy, the combined criteria for stability or thermodynamic equilibrium is expressed as  and  for parameters, entropy and volume. This is analogous to  and  condition for entropy at equilibrium. The same concept can be applied to the various thermodynamic potentials by identifying if they are convex or concave of respective their variables.
 and 
Where Helmholtz energy is a concave function of temperature and convex function of volume.
 and 
Where enthalpy is a concave function of pressure and convex function of entropy.
 and 
Where Gibbs potential is a concave function of both pressure and temperature.
In general the thermodynamic potentials (the internal energy and its Legendre transforms), are convex functions of their extrinsic variables and concave functions of intrinsic variables. The stability conditions impose that isothermal compressibility is positive and that for non-negative temperature,  .