I am coming to this question in response to scepticism about emergentism as more than an overlay (eg. SEP article).
Entropy is well established as related to relative information about systems, and as the driver of temperature change. The position and momentum of all the particles isn't enough, you also need relative uncertainties, and the system as a whole will move to the more chaotic less pure state.
Causality doesn't make sense without an arrow of time, and that seems to arise from entropy. Causality then seems to be at root information flow.
It seems that modern science is property dualist, with energy + information. And information, everything as events, is increasingly thought to be fundamental and where all other properties will be unified (ie It From Bit).
So what is the get-out I am missing? Surely information has to be causal, and emergent order has real measurable impacts on the physics, separate to a purely reductionist account?