  In this paper, we study coherence-induced state ordering with Tsallis
relative entropy of coherence, relative entropy of coherence and $l_{1}$ norm
of coherence. Firstly, we show that these measures give the same ordering for
single-qubit states with a fixed mixedness or a fixed length along the
direction $\sigma_{z}$. Secondly, we consider some special cases of high
dimensional states, we show that these measures generate the same ordering for
the set of high dimensional pure states if any two states of the set satisfy
majorization relation. Moreover, these three measures generate the same
ordering for all $X$ states with a fixed mixedness. Finally, we discuss
dynamics of coherence-induced state ordering under Markovian channels. We find
phase damping channel don't change the coherence-induced state ordering for
some single-qubit states with fixed mixedness, instead amplitude damping
channel change the coherence-induced ordering even though for single-qubit
states with fixed mixedness.
