  Generalized measures of quantum correlations are derived by taking Bayes'
rule as the only fundamental principle. The resulting quantifiers satisfy
several desirable conditions for a measure of quantum correlations and are
shown to admit operational interpretation in terms of the difference in
efficiency of quantum and classical demons in allowing for the extraction of
generalized work from a heat bath. The link with discord is established by
adopting the $q$ entropy as entropic principle. This allows us to reproduce,
within a one-parameter formalism, both the entropic and the geometric measures
of discord and physically distinguish them within the context of the
nonextensive thermodynamics. Besides offering a unified view of several
measures of correlations in terms of the Bayesian principle and its connection
with thermodynamics, our approach unveils a bridge to the nonextensive
statistical mechanics.
