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Entropy balance in holographic superconductors

In systems undergoing second order phase transitions, the temperature integral of the specific heat over temperature from zero to the critical temperature is the same in both the normal and ordered phases. This entropy balance relates the critical temperature to the distribution of degrees of freedom in the normal and ordered states. Quantum criticality and fractionalization can imply an increased number of low energy degrees of freedom in both the normal and ordered states. We explore the role of entropy balance in holographic models of superconductivity, focussing on the interplay between quantum criticality and superconductivity. We consider models with and without a ground state entropy density in the normal phase; the latter models are a new class of holographic superconductors. We explain how a normal phase entropy density manifests itself in the stable superconducting phase.