A remark on orbital free entropy

A lower estimate of the orbital free entropy ${\chi }_{\mathrm{o}\mathrm{r}\mathrm{b}}$ under unitary conjugation is proved, and it together with Voiculescu’s observation shows that the conjectural exact formula relating ${\chi }_{\mathrm{o}\mathrm{r}\mathrm{b}}$ to the free entropy $\chi$ breaks in general in contrast to the case when given random multi-variables are all hyperfinite.