It's not x86 but it is fully open source and completely open, which sounds like your goal.
Just think about your question with the following in mind
- x86 instruction set
- size and power consumption
And then type your question exactly the same into Google's search. Have a read.
Come back here again and we talk about the internets
One of the reasons could be that x86 instruction set is to big compared to the arm instruction set and one do not need such big instruction set in mobile devices anyway.
Another would be that a big instruction set needs more real estate on silicon just for the logic. But why even invest in that? Smaller instruction set but more parallel calculations is even faster for the target group.
So...
"Why does x86 consume more power than ARM? X86 processors use more registers and place a greater emphasis on performance and high throughputs. As a result, there is some excess heat production and electricity consumption. ARM devices are substantially more energy-efficient by design."
x86 is a CISC, ARM is a RISC.
So, what is the least energy hungry x86 compatible chip of all times?