Probability distribution and information theory

In the study of statistics, a given family of probability densities depending smoothly upon a parameter $theta$ can be expressed in the form

$p(x,theta)=expleft[c(x)+sum_{r}theta^{r}S_{r}(x)-psi(theta)right],$

where the variable $x$ ranges over the sample space.

In models of statistical mechanics, we generally deal with Gibbs measures in the form

$p(x,theta)=expleft[sum_{r}theta^{r}S_{r}(x)-ln(psi(theta))right],$

where the $S_{r}$ determines the form of the action and $psi(theta)=lnZ(theta)$ is gibbs free energy,
and $Z$ the partition function.

Based on the above, what is the meaning of $x$ in $Z$?