  In the classical regime, thermodynamic state transformations are governed by
the free energy. This is also called as the second law of thermodynamics.
Previous works showed that, access to a catalytic system allows us to restore
the second law in the quantum regime when we ignore coherence. However, in the
quantum regime, coherence and free energy are two independent resources.
Therefore, coherence places additional non-trivial restrictions on the the
state transformations, that remains elusive. In order to close this gap, we
isolate and study the nature of coherence, i.e.\ we assume access to a source
of free energy. We show that allowing catalysis along with a source of free
energy allows us to amplify any quantum coherence present in the quantum state
arbitrarily. Additionally, any correlations between the system and the catalyst
can be suppressed arbitrarily. Therefore, our results provide a key step in
formulating a fully general law of quantum thermodynamics.
