[math-fun] Does entropy increase because the universe is expanding?

Will someone who holds an affirmative view on this question answer the following. A chemist constructs two vessels separated by a closed stopcock.  One vessel is filled with gas, the other is evacuated.  The stopcock is opened.  In our expanding universe, the gas expands into the empty vessel until the pressures are equalized.  Entropy has increased.  What would be observed in a contracting universe?   --  Gene