I’m writing a short story where a species of aliens wipe out all life they encounter because they see life as a threat since it accelerates entropy. However, many of the methods used for destruction, like atom bombs, lasers, etc, are horribly inefficient entropy wise. What would be the best way to wipe out all life on earth in an entropy friendly way?
Turn down the sun
Your aliens add material to the sun intended to quench fusion. Less fusion slows down entropy. It has the added benefit of chilling the planets and stopping life processes.
If the aliens do not have the tech to quench a star, they could just insert an object to shade the earth, perhaps at the L1 Lagrange point or in a tight interior orbit around the star. Large flat sheets would work. Shade will cool the earth down. Possibly deep Earth life might still persist, warmed by the Earths inner heat. Surface life will freeze.
Make a virus that kills all living organisms.
An advanced, interstellar civilization probably has powerful enough computers to quickly build a virus that can kill everyone they want dead.
Have it lie dormant for a few months of years while it spreads, and then trigger at a particular time.
Just drop it down, and a few kilos of package can quickly spread to kill everyone.
Runaway greenhouse effect
Simply add more CO², methane and other greenhouse gasses. In the worst case scenario it'll be a self strengthening effect, causing the planet to increasingly heat up. This method will kill nearly all multicellular and a big chunk of unicellular life on the whole planet. It doesn't increase entropy, it actually slows it down. Less heat and energy is lost to space after is bounces off the Earth.
The remainder can be killed by specialised virusses or bacteria, that will starve themselves the moment they have consumed their intended targets.
Cooling might actually be more effective. Nearly all energy is derived from the sun. If you block this with ash clouds and the like, the planet can cool down to such an extent that even more life is lost. If not all, then nearly all. The remaining will be either at the few hot spots or living so slowly it hardly matters.
UV lamps are dangerous to all life in enough quantities. It is but one of many radiations that can be harmful. Remove the ozone layer and possibly some more and the sun will shine the world sterile. Again it might not kill all and a fraction of life will survive but that might not matter.
Store entropy in life
Instead of killing life to preserve entropy, you slow down entropy with it. Life can slow down some processes as well. Life not only uses energy, it can store it. Look at plants. They just sit in the sun and store the light. If it's stored it's use can in part be determined by the life form, increasing or decreasing consumption. With the right type of life spread around you might actually retard entropy processes, as well as store valued energy. Together with cold to slow down the processes you can get life to aid you.