A cup of tea in the hand could, at least in principle, start spontaneously boiling on one side while simultaneously freezing solid on the other. No violation of the conservation of energy need be implied, because the heat energy gained by one side of the beverage could be precisely equal to that lost by the other. But the drinker would be rather startled, because (quite apart from an unexpectedly burnt or frozen mouth) everyone knows that events of this kind do not happen. In reality, time's arrow always points in the opposite direction, towards thermal equilibrium such that all the tea is at the same temperature.