  In generalized resource theories, one aims to reformulate the problem of
deciding whether a suitable transition (typically a transition that preserves
the Gibbs state of the theory) between two given states $\rho$ and $\sigma$
exists or not, into the problem of checking whether a set of second-law--like
inequalities hold or not. The aim of these preliminary notes is to show how the
theory of statistical comparisons (in the sense of Blackwell, LeCam, and
Torgersen) can be useful in such scenarios. In particular, we propose one
construction, in which the second laws are formulated in terms of a suitable
conditional min-entropy. Though a general, fully quantum result is also
presented, stronger results are obtained for the case of qubits, and the case
of $\sigma$ commuting with the Gibbs state.
