  We consider the physical situations where the resource theories of coherence
and thermodynamics play competing roles. In particular, we study the creation
of quantum coherence using unitary operations with limited thermodynamic
resources. We first find the maximal coherence that can be created under
unitary operations starting from a thermal state and find explicitly the
unitary transformation that creates the maximal coherence. Since coherence is
created by unitary operations starting from a thermal state, it requires some
amount of energy. This motivates us to explore the trade-off between the amount
of coherence that can be created and the energy cost of the unitary process. We
find the maximal achievable coherence under the constraint on the available
energy. Additionally, we compare the maximal coherence and the maximal total
correlation that can be created under unitary transformations with the same
available energy at our disposal. We find that when maximal coherence is
created with limited energy, the total correlation created in the process is
upper bounded by the maximal coherence and vice versa. For two qubit systems we
show that there does not exist any unitary transformation that creates maximal
coherence and maximal total correlation simultaneously with a limited energy
cost.
