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Correlations disguised in various forms underlie a host of importantphenomena in classical and quantum systems, such as information and energyexchanges. The quantum mutual information and the norm of the correlationmatrix are both considered as proper measures of total correlations. Wedemonstrate that, when applied to the same system, these two measures canactually show significantly different behavior except at least in two limitingcases: when there are no correlations and when there is maximal quantumentanglement. We further quantify the discrepancy by providing analyticformulas for time derivatives of the measures for an interacting bipartitesystem evolving unitarily. We argue that to properly account for correlations,one should consider the full information provided by the correlation matrix(and reduced states of the subsystems). Scalar quantities such as the norm ofthe correlation matrix or the quantum mutual information can only capture apart of the complex features of correlations. As a concrete example, we showthat in describing heat exchange associated with correlations, neither of thesequantities can fully capture the underlying physics.

Mutual Information is not a Reliable Measure for Variations in Total Correlations