14  Adiabatic Processes

The word adiabatic is another term that suffers from multiple inconsistent meanings. The situation is summarized in figure 14.1.

Figure 14.1: Multiple Definitions of Adiabatic

1. Some thoughtful experts use “adiabatic” to denote a process where no entropy is transferred across the boundary of the region of interest. This was probably the original meaning, according to several lines of evidence, including the Greek etymology: α + δια + βατoς = not passing across. As a corollary, we conclude the entropy of the region does not decrease.
2. Other thoughtful experts refer to the adiabatic approximation (in contrast to the sudden approximation) to describe a perturbation carried out sufficiently gently that each initial state can be identified with a corresponding final state, and the occupation number of each state is preserved during the process. As a corollary, we conclude that the entropy of the region does not change.
3. Dictionaries and textbooks commonly define “adiabatic” to mean no flow of entropy across the boundary and no creation of entropy.

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:

• If you mean thermally insulated, say thermally insulated.
• If you mean a non-sudden perturbation, say non-sudden or gentle.
• If you mean isentropic, say isentropic.
• Instead of the nouns “adiabat” or “adiabatic line”, say “contour of constant entropy”.