Is there a way to add applications/processes to the Power Nap function on a Mac? In other words, instead of just the default Time Machine, Mail, etc. you can make it run other applications too. I am running a Mac Mini with OS X Yosemite.
So far as I can tell, the answer is no. I can't find any mention of public APIs for developers to leverage Power Nap.
What did you have in mind? You could also put in an enhancement request at Apple.