In this paper we calculate the leading-order correction due to small statistical fluctuations around equilibrium to the Bekenstein–Hawking entropy formula for the Ach´ucarro–Oritz black hole, which is the most general two-dimensional black hole derived from the three-dimensional rotating Ba˜nados–Teitelboim– Zanelli black hole. Then we obtain the same correction to the Cardy–Verlinde entropy formula (which is supposed to be an entropy formula of conformal field theory in any number of dimensions).