One problem related to battery has been reported for the 2011 Jeep Wrangler. The most recently reported issues are listed below.
I went to a Jeep jamboree on the weekend of September 17th and as I was driving to go wash my Jeep my Jeep first speed up and I couldn't get it to slow down then I smelled a burning smell and then dashboard started having trouble lights come on so I got it off the highway as I exited the highway I saw smoke coming from under the hood so I stopped immediately and opened the hood after shutting it off and saw it coming from the main fuse block grabbed some tools to disconnect the battery but by then it started to burn so I poured water on the fuse block put it out and called a tow truck took it to tri star Jeep in uniontown, PA they got it fixed after almost 2 weeks and on the way home it started again and I caught it earlier but this time I had to pay out of pocket. Ever since those 2 episodes it's had lots of electrical problems and it just never stops.