Bulk-boundary interaction and the second law in Hořava-Lifshitz cosmology

By defining Q as a function which realizes the energy transference between the bulk and the boundary of spacetime, as we interpret it here in the framework of the flat case of Hořava-Lifshitz cosmology, we discuss the validity of the second law of thermodynamics in light of the sign changes of Q (changes in the direction of energy transference) and its consequences through the cosmic evolution, in particular, whether the thermal equilibrium between the bulk and the boundary is reached or not. Additionally, we discuss possible phase transitions experienced by the bulk and the boundary (seen as sign changes in their heat capacities) through the cosmic evolution. The energy density in the bulk is modeled under a holographic perspective. As far as we know, currently there is not observational data on the bulk-boundary interaction.