When studying Thermodynamics, we make much use of adiabatic processes where a change is made so fast that no significant heat can flow. For example, the compression stroke of a diesel engine.

In quantum mechanics, it seems they turn the definition on its head, adiabatic is defined as a change to the system that occurs gradually compared to the evolution of the unperturbed system. An example is a pendulum of period T with its length changing slowly compared to T.

Are these two definitions somehow the same? Are they even related? I can't make sense of this.