Thermal fluctuations to the thermodynamics of a non-rotating BTZ black hole

Abstract

We discuss the effect of small statistical thermal fluctuations around the equilibrium of the thermodynamics of a small non-rotating BTZ black hole. This is done by evaluating the leading-order corrections to the thermodynamical equations of state, namely entropy, free energy, internal energy, pressure, enthalpy, Gibbs free energy, and specific heat, quantitatively. In order to analyze the effects of perturbations on the thermodynamics, we plot various graphs and compare corrected and non-corrected thermodynamic quantities with respect to the event horizon radius of a non-rotating BTZ black hole. We also derive the first-order corrections to isothermal compressibility.