# Partition Function- Are the energies of the individual microstates, free energies?

$$Z=\sum_i e^{-\beta E_i}$$ I am relatively new to statistical mechanics, and I am wondering if the individual energies ($E_i$) in the equation above are free energies associated with each microstate? If it is, would it be Gibb's Free Energy or Helmholtz's Free Energy?

• It's not free energy, it's energy. Feb 27, 2018 at 15:22

No, the $E_i$s are energies. In statistical mechanics it can be show (see for example here) that the Helmotz's free energy $F$ is related to the partition function of the system in the following way $$F = -kT\log Z$$ and all other thermodynamic relations, e.g. that with the Gibbs's free energy, can be found starting from it.