General logarithmic corrections to black-hole entropy

We compute leading-order corrections to the entropy of any thermodynamic system due to small statistical fluctuations around equilibrium. When applied to black holes, these corrections are shown to be of the form −k ln(Area). For BTZ black holes, k = 3/2, as found earlier. We extend the result to anti-de Sitter Schwarzschild and Reissner–Nordström black holes in arbitrary dimensions. Finally we examine the role of conformal field theory in black-hole entropy and its corrections.