  Reliably computing the free energy in a gauge theory like QCD is a
challenging and resource-demanding endeavor. As an alternative, we explore here
the possibility to obtain the associated thermodynamic anomaly by exploiting
its relation to the Tan contact. Optimally, this would reduce the determination
of the free energy to a high-precision calculation of two-point correlators. We
study this possibility using the lattice and functional methods and compare
them to the expected behavior for the SU(2) Yang-Mills case.
