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The aim of this paper is to study the local and the global thermodynamicproperties of the 3-dimensional rotating Gauss-Bonnet black hole. To this endwe consider the conditions for local and global thermodynamic stability of thesolution in a given ensemble of state quantities. Concerning the local analysiswe found the regions of stability for every physical specific heat togetherwith the existing Davies curves. Another central result is the generalizationof the notion of global thermodynamic stability, known from the standardthermodynamics, to describe the global equilibrium of black holes. The newapproach consists of applying specific Legendre transformation of the energy orthe entropy to find the natural thermodynamic potential for the given ensembleof macro parameters. The global stability analysis, restricted to the weekpositivity conjecture is based on the properties of the new thermodynamicpotential. The advantage of this method is that it allows one to chosedifferent potentials, corresponding to different constraints to which thesystem may be subjected. Finally, we find it natural to impose globalthermodynamic stability only where local one exists for the given black holesolution.

Global and local thermodynamics of the (2+1)-dimensional rotating Gauss-Bonnet black hole