The proof in thermodynamics that heat flows from a hotter to a colder body relies on the assumption of "molecular chaos" - basically that systems and their environments have negligible correlations. I will discuss some of the strange things, such as negative heat flow, that can happen when correlations are present - and explain how these can provide a witness to quantum entanglement. Along the way I will also discuss a proposal by Maccone for a "quantum resolution to the arrow of time".