Thermodynamic studies of different black holes with modifications of entropy

In recent years, the thermodynamic properties of black holes are topics of interests. We investigate the thermodynamic properties like surface gravity and Hawking temperature on event horizon of regular black holes viz. Hayward Class and asymptotically AdS (Anti-de Sitter) black holes. We also analyze the thermodynamic volume and naive geometric volume of asymptotically AdS black holes and show that the entropy of these black holes is simply the ratio of the naive geometric volume to thermodynamic volume. We plot the different graphs and interpret them physically. We derive the 'cosmic-Censorship-Inequality' for both type of black holes. Moreover, we calculate the thermal heat capacity of aforesaid black holes and study their stabilities in different regimes. Finally, we compute the logarithmic correction to the entropy for both the black holes considering the quantum fluctuations around the thermal equilibrium and study the corresponding thermodynamics.