Thermodynamics of Dyonic NUT Charged Black Holes with Entropy as Noether Charge

We investigate the thermodynamic behaviour of Lorentzian Dyonic Taub-NUT Black Hole spacetimes. We consider two possibilities in their description: one in which their entropy is interpreted to be one quarter of the horizon area (the horizon entropy), and another in which the Misner string also contributes to the entropy (the Noether charge entropy). We find that there can be as many as three extremal black holes (or as few as zero) depending on the choice of parameters, and that the dependence of the free energy on temperature -- and the resultant phase behaviour -- depends very much on which of these situations holds. Some of the phase behaviour we observe holds regardless of which interpretation of the entropy holds. However another class of phase transition structures occurs only if the Noether charge interpretation of the entropy is adopted.