  In this expository note, we study the second variation of Perelman's entropy
on the space of Kahler metrics at a K\"ahler-Ricci soliton. We prove that the
entropy is stable in the sense of variations. In particular, Perelman's entropy
is stable along the K\"ahler-Ricci flow. The Chinese version of this note has
appeared in a volume in honor of professor K.C.Chang (Scientia Sinica Math., 46
(2016), 685-696).
