A thermodynamic classification of real numbers

TextA new classification scheme for real numbers is given, motivated by ideas from statistical mechanics in general and work of Knauf (1993) [16] and Fiala and Kleban (2005) [8] in particular. Critical for this classification of a real number will be the Diophantine properties of its continued fraction expansion.VideoFor a video summary of this paper, please click here or visit http://www.youtube.com/watch?v=qnPF2QS4cRg.