  In the context of irreversible dynamics, associating to a physical process
its intuitive reverse can result to be a quite ambiguous task. It is a standard
choice to define the reverse process using Bayes' theorem, but, in general,
this choice is not optimal. In this work we explore whether it is possible to
characterise an optimal reverse map building from the concept of state
retrieval maps. In doing so, we propose a set of principles that state
retrieval maps should satisfy. We find out that the Bayes inspired reverse is
just one case in a whole class of possible choices, which can be optimised to
give a map retrieving the initial state more precisely than the Bayes rule. Our
analysis has the advantage of naturally extending to the quantum regime. In
fact, we find a class of reverse transformations containing the Petz recovery
map as a particular case, corroborating its interpretation as quantum analogue
of the Bayes retrieval. Finally, we present numerical evidences that by adding
a single extra axiom one can isolate the usual reverse process derived from
Bayes' theorem.
