Entropy is equal to its temperature derivative, while pressure is equal to its volume derivative.
Calculations of the phase transitions for the Ising Model use this quantity because the magnetic field is a natural variable. For a perturbed system, the variational principle gives the upper bound of this as the expectation value of the unperturbed Hamiltonian. For an ideal gas, it features a natural logarithm of concentration over quantum concentration. Entropy is equal to its temperature derivative, while pressure is equal to its volume derivative. The Bogoliubov inequality gives a bound to it and this quantity is very useful in the canonical ensemble because volume and temperature are its natural variables. Thus, it is proportional to temperature times the (*) natural logarithm of the partition function. This quantity equals the product of temperature and entropy subtracted from the internal energy. Represented as A or F, for 10 points, is which type of free energy named for a German scientist?
Calculations of the phase transitions for the Ising Model use this quantity because the magnetic field is a natural variable.
Helmholtz Free Energy [accept Helmholtz only after mention of free energy; prompt on partial answer; prompt on A; prompt on F]