Should note that these are similar in specs to Arduinos, ie. only a few kilobytes of memory and a processor similar to a Cortex-M0. You won't be able to run Linux on them.
For example here is how to get Ubuntu linux to boot on an 8-bit AVR ATmega1284p, by emulating ARMv5: http://dmitry.gr/index.php?proj=07.+Linux+on+8bit&r=05.Proje...
And as most people know, but if they didn't, here is linux on a hard drive microcontroller http://spritesmods.com/?art=hddhack&page=1
And probably the best option for performance, if it can be ported over, uClinux doesn't require an mmu. http://www.uclinux.org/ports/
That's awesome, even if it takes 3 hours to boot. :-P Almost everything can be considered a Turing machine if you're patient enough.
Notable omissions include: no DMA, no I2C, no ADC/DAC, and no good documentation. (The documentation that is available is inconsistent and poorly written. Some of the documentation references a nonexistent third SPI peripheral, for instance.)
The arduino has a DAC?
> no I2C
Well, I'm out then. That's a big one.
and is also not supported by any Arduino libraries to my knowledge, even with additional board support packages.
Granted, a very high clocked Cortex-M0+. The clocks are about two and a half times the highest clocked M0+es on the market AFAICT. What it lacks is peripherals (especially ADC).
With 16K cache. I'm not sure how you ensure consistent performance though - make sure your code will all fit in 16K, but is that enough? And what about the first time through?
16k cache is likely enough to ensure stable performance of any given function and any tight loops you're using but will probably not be enough for the entire program so you'll still have misses that cause slow downs but it'll probably not be terribly noticeable unless you're trying to ensure timing over large functions.