I have a similar issue. My phone was fully charged and not doing anything on it, including the screen. I checked it after about 20 minutes to get ready to go some where, and saw it was down to 75%. When I got to my destination, it was down to 47%, (a ten minute drive)and I hadn't used it. (the phone itself seemed hotter than normal, especially because I wasn't using any apps) within an hour it was down to 4%. I took it to my carrier to look at, they did some basic checks and recommended I take it to Batteries Plus to have the battery check (warranty used up) or possibly a problem with the phone itself (still under a warranty plan)
Long story short, the battery life is at 73%. They told me about an app, "advanced task killer" for droids, and it can help with extending daily battery life by, killing background app and tasks without having to turn off or clear cache for each app.
That said, the problem still exists and even "killing" tasks on apps, my battery life went from 100% to dead in three hours, and sent two texts in that time.
The Batteries Plus people mentioned to try to plug in your phone at about 30% power and only until charged 100%.(they did an overnight check of the battery) They told me that charging my battery for too long can shorten the battery life of a cell phone battery. Charging below it 30%, or longer than the threeish hours it takes to charge, (for example overnight) shortens the battery life. So no more charging the battery for 8ish hours.
The Batteries Plus store have had a lot of people coming in with the Samsung S3 lately, asking for new batteries. (recall in the near future?)
I personally would venture to guess that it is a hardware malfunction overheating the battery, based on how this is sucking power so fast with or without apps in use.
(I am an o--l--d customer service rep from the mobile phone era of 20lb portable devices or "car phones" that would "SAT time out or FADE" aka overheat. seems like the same behaviors I used to see a looong time ago, when the battery was a separate part of the device because it was connected to the vehicle.)
We are looking into getting the phone replaced, hopefully under warranty with no deductible, and not a used, refurbished phone with the same issues.