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
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]