Pre-Cooling Strategy Can Generate Exponentially Faster Heating*

What is the fastest way to heat a system which is coupled to a temperature controlled oven? The intuitive answer is to use only the hottest temperature available. However, we show that in some cases it is possible to achieve an exponentially faster heating, and propose a strategy to find the optimal protocol. Surprisingly, this protocol can have a pre-cooling stage: cooling the system before heating it shortens the heating time significantly. This approach can be applied to many-body systems, as we demonstrate in the 2D antiferromagnet Ising model.