Why are only five out of eight possible thermodynamic potentials important?

[ati]

Starting from the equation

dE=tdS-PdV+$$\mu$$ dN

It is straightforward to derive all 8 possible thermodynamic potentials. My question is the following: Why are the only important potentials

Entropy
Helmholtz free energy
Enthalpy
Gibbs free energy
Grand potential ?

Why aren't the other three as relevant as these?

Thanks for your help
-Ati

 

[Mapes]

Hi ati, welcome to PF. Systems with constant entropy or constant chemical potential are somewhat less familiar to us than systems with constant temperature or constant particle number. Potentials are still defined and used for the more exotic systems even though they aren't mentioned in most thermodynamics texts. Also, note that one of the potentials (E-TS+PV-$\mu$N) is identically zero!

You may be interested in reading Graben and Ray's "Eight physical systems of thermodynamics, statistical mechanics, and computer simulations" Molecular Physics 80(5) (1993).