Corrected thermodynamics of $(2+1)D$ black hole conformally coupled to a massless scalar

We study the corrected entropy due to thermal fluctuation and their effect on the thermodynamics of a conformally dressed black hole in three dimensions. We find that the thermal fluctuation affects the entropy significantly for small black holes. Various corrected thermodynamical variables are also calculated for this black hole. We observe that thermal fluctuation on the thermodynamics of a small conformal black hole has a significant effect. We also analyse the stability of black hole under the effect of thermal fluctuation. Due to thermal fluctuation, instability occurs in the system of small conformal black holes. Isothermal compressibility is also studied for this black hole which diverges for the equilibrium state of the system.