Intuitively, one can say that a dynamical system is *alive* if one can build a [universal Turing machine][1] inside.
So, Conway's [Game of Life][2] is alive and [shift space][3] should be dead.

I fail to make this definition precise. 
Please let me know if someone made it (or at least was trying to).
*(It is  nice if you can make a def. 
BUT I'm mostly interested if you saw such definition in the literature.)*

**Comments:**

 - There is a [relateted question][4], and it links to [this paper][5] by Graça--Campagnolo--Buescu (thanks to Joel).


  [1]: http://en.wikipedia.org/wiki/Universal_Turing_machine
  [2]: http://en.wikipedia.org/wiki/Conway's_Game_of_Life
  [3]: http://en.wikipedia.org/wiki/Shift_space
  [4]: http://mathoverflow.net/questions/15309
  [5]: http://wslc.math.ist.utl.pt/ftp/pub/GracaDS/05-GCB-stable.pdf