When you are standing with one leg in front of you and the other behind (i.e. in an Empty stance) and, using only your chest, you push something ahead of you (i.e. moving into a Bow stance), your centre moves towards the object that you’re pushing.
The maths of this is definitely not something I’m confident about: First of all, there will be some ratio of relative forward to backward power-generation that I am sure someone will correct me on, but it’s possibly 2:1 (the rear leg pushing into the ground behind you, – the backward movement against the forward movement of the body enhanced by the use of the arms). Secondly there’s the over-all generation of power produced through the hands. I really should have concentrated better in physics at school. So what has this to do with opening and closing? The first point is that both the forward and backward movements for the push come from the centre.