a modified thermodynamics of rotating and charged btz black hole

We present the thermodynamics of a charged and rotating btz black holes here. in particular, we derive expressions for various macroscopic thermal quantities such as entropy, hawking temperature, helmholtz free energy, internal energy, enthalpy, gibbs free energy, and specific heat.to study the effects of small statistical thermal fluctuations around the equilibrium on thermodynamics, we calculated the leading-order corrections to the variousthermodynamical potentials of charged and rotating btz black hole and do comparative analysis for the fixed values of charge and angular momentum.