The incredible Robert Murray Smith has done it again! In this video he describes
how clay mixed with water will boil (this works best with Zeolite 13x other clays may not work)
and can be used to power a peltier element quite strongly. Then after the water evaporates
just add more water and run it again! Now you may not see this as a self runner, but it seems
quite possible to use the peltier to run a device to help evaporate the water and if the device
is in an airtight container, the evaporated water will condense and start the cycle over again.
Or you could just let the water evaporate on its own and it will condense and restart the cycle.
This can be repeated many times.
In the comments Robert says they have systems set up to use this method that will last up to 20 years!
Also in the comments are at least two suggestions how to make this a self runner.
This will also work very nicely with a nitinol engine or a stirling device.
https://www.youtube.com/watch?v=jPGP1R7k-zQ
if you don't want to sit through Roberts lecture, the fun part begins at 3.50 on
the video when he adds water to the dry clay.