Thermodynamics of Reissner-Nordstrom-anti-de Sitter black holes in the   grand canonical ensemble
  The thermodynamical properties of the Reissner-Nordstr\"om-anti-de Sitter black hole in the grand canonical ensemble are investigated using York's formalism. The black hole is enclosed in a cavity with finite radius where the temperature and electrostatic potential are fixed. The boundary conditions allow us to compute the relevant thermodynamical quantities, e.g. thermal energy, entropy and charge. The stability conditions imply that there are thermodynamically stable black hole solutions, under certain conditions. Instantons with negative heat capacity are also found. 
Claudia Pe\c{c}a, Jose' P. S. Lemos