  Given a probability density $P({\bf x}|{\boldsymbol \lambda})$, where $\bf x$
represents continuous degrees of freedom and $\lambda$ a set of parameters, it
is possible to construct a general identity relating expectations of observable
quantities, which is a generalization of the equipartition theorem in
Thermodynamics.
  In this work we explore some of the consequences of this relation, both in
the context of sampling distributions and Bayesian posteriors, and how it can
be used to extract some information without the need for explicit calculation
of the partition function (or the Bayesian evidence, in the case of posterior
expectations). Together with the general family of fluctuation theorems it
constitutes a powerful tool for Bayesian/MaxEnt problems.
