This talk was recorded at the 2nd International Conference on
Holography and its Applications
(ICHA2 2023)

Abstract. We derive the corrected entropy due to the thermal fluctuation and its effects on the
thermodynamic parameters of the three-dimensional AdS spacetime black hole conformally coupled to
massless scalar field. We find that the thermal fluctuation has significant effects on the entropy of the
small black hole. We further investigate the attributions of the corrected entropy on the corrected
thermodynamic parameters like Helmholtz free energy, Internal energy, Pressure, Enthalpy, Gibbs free
energy. We find that thermal fluctuation has significant effects on the thermodynamics of small
conformal black hole. At the end we analyze the stability of the conformal black hole by isothermal
compressibility and find that the instability occurs for the small conformal black holes.


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