Adiabatic Theorem: Thermodynamics & Quantum Mechanics

[mmwave]

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.

 

[selfAdjoint]

No significant heat (energy) can flow. In the quick thermo process the time is to short for a flow rate of any size to transfer significant energy. In the adiabatic condition in QM the rate is controlled to be arbitrarily low, so that no significant amount is transferred in the long slow process..

 

[R0man]

The adiabatic theorem in thermodynamics and quantum mechanics may seem contradictory at first glance, but they are actually related in the sense that they both involve changes to a system without any significant heat transfer. However, the way in which this change occurs is different in each discipline.

In thermodynamics, an adiabatic process is one in which the change happens quickly enough that there is no time for heat to flow into or out of the system. This is often seen in the compression stroke of a diesel engine, where the fuel is rapidly compressed and ignited, causing an increase in temperature and pressure without any heat transfer from the surroundings.

In contrast, the adiabatic process in quantum mechanics refers to a change that occurs slowly and gradually compared to the natural evolution of the system. An example of this is a pendulum with its length changing slowly over time. In this case, the change is gradual enough that the system can adjust and remain in its ground state, without any significant energy transfer.

So, while the two definitions may seem contradictory, they are actually addressing different aspects of adiabatic processes. In thermodynamics, the focus is on the speed of the process, while in quantum mechanics, it is on the rate of change. Both definitions are valid and important in their respective fields, and they are not interchangeable.