Describing the ground state of quantum systems through statistical mechanics

We present a statistical mechanics description to study the ground state of quantum systems. In this approach, averages for the complete system are calculated over the non-interacting energy levels. Taking a different interaction parameter, the particles of the system fall into non-interacting microstates, corresponding to different occupation probabilities for these energy levels. Using this novel thermodynamic interpretation we study the Hubbard model for the case of two electrons in two sites and for the half-filled band on a one-dimensional lattice. We show that the form of the entropy depends on the specific system considered.