The universe expands. Entropy increases.
In an article on the arrow of time, Thomas Gold suggested the two are related (p. 86, 1958 Solvay Institute, The structure and evolution of the universe). As the universe ages (entropy increases) the available degrees of freedom for the constituents of the universe increase. The possible number of states of the universe increases along with entropy. With more states, more of those states might include the emergence of life.
On the other hand, as matter becomes more dispersed in some later stage of the expansion, the chances of life emerging may diminish. In the age of the universe there may be a Goldilocks time era, not too early and not too late.
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