Geometrically Frustrated Systems which are as Singles Hotter Than in Company

We show that an ensemble of thermally weakly coupled geometrically frustrated systems (GFSs), which are constraint to reside at negative Boltzmann temperatures, is in equilibrium cooler than its constituents, and may even exhibit positive temperatures at low energies. The challenge for the second law of thermodynamics arising from potential heat flow related to the Boltzmann temperature gradient between a GFS and its ensemble is resolved by considering the energy fluctuations above the ground state, i.e. the most probable state of a GFS. They are comprised in the canonical temperature, derived from information theory. Whereas the Boltzmann temperature gradient reveals the direction of the stochastic drift of the most probable state of a GFS within its ensemble, canonical temperature gradients define that of heat flow.