  The amount of correlation attainable between the components of a quantum
system is constrained if the system is closed. We provide some examples,
largely from the field of quantum thermodynamics, where knowing the maximal
possible variation in correlations is useful. The optimization problem it
raises requires us to search for the maximally and minimally correlated states
on a unitary orbit, with and without energy conservation. This is fully
solvable for the smallest system of two qubits. For larger systems the problem
is reduced to a manageable, classical optimization.
