For the rotating quantum BTZ black hole, the paper derives path-dependent heat capacities at constant pressure and volume with multiple positive and negative branches.
In the case of fixed z, the heat capacity is Cp,z(ν, z, α) = T (ν, z, α) ∂S ∂α ν,z ∂α ∂T ν,z
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Specific Heats for Rotating Quantum BTZ Black Holes in Extended Thermodynamics
For the rotating quantum BTZ black hole, the paper derives path-dependent heat capacities at constant pressure and volume with multiple positive and negative branches.