What Does a Partition Function Tell You

The partition function is the connection between macroscopic thermodynamic properties and microscopic models. It is a sum of Boltzmann factors e kT that specify how particles are partitioned throughout the accessible states. For many typical problems, the ground state has zero energy, Ei =0. In those 

Boltzmann distribution law. At low temperatures T, only the lowest energy states j are populated. Increasing T increases popuiations of higher energy states. The distribution is exponential. 

At the other extreme, as the energy intervals become large or as the temperature approaches zero, the particles occupy only the ground state  

In this case, only the ground state becomes accessible. 

The number of effectively accessible states is not the same as the number of accessible states, which is always t. The number t is fixed by the underlying physics of the system. In contrast, the effective accessibility Q also depends on the temperature. 

---