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On Einstein-non linear-Maxwell-Yukawa de-Sitter black hole thermodynamics

We investigate the thermodynamics of the Einstein-non linear-Maxwell-Yukawa black hole solution in de-Sitter spacetime. After presenting the black hole solution and its horizons, we use different thermodynamics points of view to probe the phase structure of such a black hole, ranging from local, global thermodynamics to the effective thermodynamics formalism with two horizons. Our analysis shows that the black hole can undergo a thermal phase transition between an unstable phase and stable phase. These results are consolidated by our proposal of generalizing effective thermodynamics to three horizons black holes. As by product, we find that the effective temperatures behave as an association of ohmic resistances in an electric circuit, which may reveal a possible analogy between the electric and thermodynamic systems.