quantum mechanics - commutators in an uncertainty relationship derived from a partition function?

The maximum information principle for the discrete case gives rise to a partition function (>>> see details here)

$$Z(\lambda_1,\ldots, \lambda_m) = \sum_{i=1}^n \exp\left[\lambda_1 f_1(x_i) + \cdots + \lambda_m f_m(x_i)\right]$$

Question: is it possible to identify from this equation commutators in an uncertainty relationship?