  Quantum obesity (QO) is new function used to quantify quantum correlations
beyond entanglement, which also works as a witness for entanglement. Thanks to
its analyticity for arbitrary state of bipartite systems, it represents an
advantage with respect to other quantum correlations, like quantum discord for
example. In this work we show that QO is a fundamental quantity to observe
signature of quantum phase transitions. We also describe a mechanism based on
local filtering operations able to intensify the critical behavior of the QO
near to the transition point. To this end, we introduce a theorem stating how
QO changes under local quantum operations and classical communications. This
work opens perspective for the characterization of new phenomena in quantum
critical systems through the analytically computable pairwise QO.
