when two isolated systems in separate but nearby regions of space, each in thermodynamic equilibrium in itself (but not necessarily in equilibrium with each other at first) are at some time allowed to interact, breaking the isolation that separates the two systems, allowing them to exchange matter or energy, they will eventually reach a mutual thermodynamic equilibrium. The sum of the entropies of the initial, isolated systems is less than or equal to the entropy of the final combination of exchanging systems. In the process of reaching a new thermodynamic equilibrium, total entropy has increased, or at least has not decreased.
What is true for heat may, I suggest, also be true for coolness. I'm not mathematician enough to express this as a formula, but consider the following example. In 1974, Prince Charles (System A) declared that his favourite pop group was The Three Degrees (System B). Prior to this declaration neither system possessed a great deal of coolness, although it was observed that System B was still definitely cooler than System A. As a result of the royal preference being made known the two systems interacted, and there was a transfer of coolness. In short, the declaration made Prince Charles slightly cooler than he had been before (although to such a small extent that the instruments of the 1970s had difficulty detecting the effect); while The Three Degrees became less cool.
But observe! The amount of coolth lost by the Three Degrees was an order of magnitude greater than that gained by Prince Charles. In other words, the total amount of coolness in the two systems was less at the end of the interaction than it had been at the beginning.
This is not an isolated example: look at David Cameron's endorsement of The Killers - and I'm sure others will quickly suggest themselves. I propose to call this phenomenon coolness entropy, and predict that the universe will eventually experience a "coolness death" in which all music will end up sounding like Val Doonican.