The word adiabatic is another term that suffers from multiple inconsistent meanings. The situation is summarized in figure 14.1.
In the dream-world where only reversible processes need be considered, definitions (1) and (2) are equivalent, but that’s not much help to us in the real world.
Also note that when discussing energy, the corresponding ambiguity cannot arise. Energy can never be created or destroyed, so if there is no transfer across the boundary, there is no change.
As an example where the first definition (no flow) applies, but the second definition (occupation numbers preserved) does not, see reference 41. It speaks of an irreversible adiabatic process, which makes sense in context, but is clearly inconsistent with the second meaning. This is represented by point (1) in the figure.
As an example where the second definition applies but the first definition does not, consider the refrigeration technique known as adiabatic demagnetization. The demagnetization is carried out gently, so that the notion of corresponding states applies to it. If the system were isolated, this would cause the temperature of the spin system to decrease. The interesting thing is that people still call it adiabatic demagnetization even when the spin system is not isolated. Specifically, consider the subcase where there is a steady flow of heat inward across the boundary of the system, balanced by a steady demagnetization, so as to maintain constant temperature. Lots of entropy is flowing across the boundary, violating the first definition, but it is still called adiabatic demagnetization in accordance with the second definition. This subcase is represented by point (2) in the diagram.
As an example where the second definition applies, and we choose not to violate the first definition, consider the NMR technique known as “adiabatic fast passage”. The word “adiabatic” tells us the process is slow enough that there will be corresponding states and occupation numbers will be preserved. Evidently in this context the notion of no entropy flow across the boundary is not implied by the word “adiabatic”, so the word “fast” is adjoined, telling us that the process is sufficiently fast that not much entropy does cross the boundary. To repeat: adiabatic fast passage involves both ideas: it must be both “fast enough” and “slow enough”. This is represented by point (3) in the diagram.
My recommendation is to avoid using the term adiabatic whenever possible. Some constructive suggestions include: