Perelmans W-functional and stability of Kahler-Ricci flow

In this expository note, we study the second variation of Perelmans entropy on the space of Kahler metrics at a Kahler-Ricci soliton. We prove that the entropy is stable in the sense of variations. In particular, Perelmans entropy is stable along the Kahler-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).