Also known as a Massieu, Planck, or Massieu–Planck potentials (or functions), or (rarely) free information.
In statistical mechanics, free entropies frequently appear as the logarithm of a partition function.
The Onsager reciprocal relations in particular, are developed in terms of entropic potentials.
Note that the use of the terms "Massieu" and "Planck" for explicit Massieu-Planck potentials are somewhat obscure and ambiguous.
By the definition of a total differential, From the equations of state, The differentials in the above equation are all of extensive variables, so they may be integrated to yield Starting over at the definition of
and taking the total differential, we have via a Legendre transform (and the chain rule) The above differentials are not all of extensive variables, so the equation may not be directly integrated.