Coherence as entropy increment for Tsallis and Rényi entropies

Relative entropy of coherence can be written as an difference the original state and incoherent closest to it when measured by relative entropy. The natural question is, if we generalize this situation Tsallis or Rényi entropies, would define good measures? In other words, a between entropies Taking instead entropy, leads well-known distance-based coherence, which means expression defined measure. Interestingly, show that does not generate even genuine monotone, unless is under very restrictive class operations. Additionally, provide continuity estimate for coherence. Furthermore, present two measures based on