  We study the limitations on coherence evolutions under the constraints of
thermodynamic laws, and focus on the optimal thermal operations (TO) reaching
the bounds. For qubit case, we find a thermal operation involving only a
single-mode reservoir (STO) which maintains the maximum coherence allowed by
general TO. For higher dimensions, we derive general bounds on coherence
merging under TO, and find STO to reach the bounds. By applying the bound to a
two-qubit system, we prove that erasing correlations while preserving the
marginal states is not free in the resource theory of thermodynamics. Due to
the simple structure of STO and its strong ability in coherence processing, our
results shed light on both theoretical and experimental studies in the field of
thermodynamics for small quantum systems.
