  We investigate sudden change (SC) behaviors of the distance-based measures of
geometric quantum discords (GQDs) for two non-interacting qubits subject to the
two-sided and the one-sided thermal reservoirs. We found that the GQDs defined
by different distances exhibit different SCs, and thus the SCs are the combined
result of the chosen discord measure and the property of a state. We also found
that the thermal reservoir may generate states having different orderings
related to different GQDs. These inherent differences of the GQDs reveal that
they are incompatible in characterizing quantum correlations both
quantitatively and qualitatively.
