I'm somewhat familiar with Barbour's work, which tries to reformulate gravity as a theory of 3-geometries instead of 4-geometries. Basically, you can do this by moving additional complexity into the lagrangian. Barbour's work is hard to get into because he has had various versions of this theory (Shape Dynamics) over the years and some of them are classical models, some are curved spacetime, some are more effective at being totally relational than others, etc.

Anyway, its true that something he calls the complexity increases forever in his more recent models, this is just an expression chosen to make the dynamics work out. Even Barbour says this is not necessarily related to the sort of complexity life has. And it depends on the universe being an open systems.