Will a Large Complex System be a Maxwell Demon?

Emerging evidence suggests that physical systems operating as Maxwell demons, in which some subsystem of a larger system extracts heat energy from its environment in an apparent local violation of the second law, are commonplace throughout biology. Should these findings surprise us, or is Maxwell demon behavior inevitable in sufficiently large complex systems? In this Letter we pose the question of how likely it is that a random stochastic system with many degrees of freedom will operate as a Maxwell demon, considering null models for both continuous and discrete random dynamics. Our results show the probability of a finding a demon decreases at least exponentially, and in some cases double-exponentially, with the number of degrees of freedom, ultimately suggesting that large complex demons can only arise through a process of selection.