I wrote a post here
which followed up on another post on entropy transport. The big generator of entropy is just the thermalization of sunlight. Plants are able to in effect divert some of this, creating photosynthesis products which have free energy. That's what we all live on. Of course, when we've done all that, we've released the entropy, or lost the free energy, that the plants saved. So it's only a postponement.
The export of entropy is interesting. It all does have to get exported, and the mechanism is that the flux of heat out, which balances in, leaves at a lower temperature than it came. If it can be persuaded to leave even cooler, that's more free energy available. That's not necessarily good - it would probably encourage atmospheric mischief.