Editing Adiabatic process (section)

==Divergent usages of the word ''adiabatic''==
This present article is written from the viewpoint of macroscopic thermodynamics, and the word ''adiabatic'' is used in this article in the traditional way of thermodynamics, introduced by Rankine. It is pointed out in the present article that, for example, if a compression of a gas is rapid, then there is little time for heat transfer to occur, even when the gas is not adiabatically isolated by a definite wall. In this sense, a rapid compression of a gas is sometimes approximately or loosely said to be ''adiabatic'', though often far from isentropic, even when the gas is not adiabatically isolated by a definite wall.

Some authors, like [[Brian Pippard|Pippard]], recommend using "adiathermal" to refer to processes where no heat-exchange occurs (such as Joule expansion), and "adiabatic" to reversible quasi-static adiathermal processes (so that rapid compression of a gas is ''not'' "adiabatic").<ref>{{Cite book |last=Pippard |first=Alfred B. |title=Elements of classical thermodynamics: for advanced students of physics |date=1981 |publisher=Cambridge University Press |isbn=978-0-521-09101-5 |location=Cambridge, England}}</ref> And [[Keith J. Laidler|Laidler]] has summarized the complicated etymology of "adiabatic".<ref>{{Cite journal |last=Laidler |first=Keith J. |date=1994-03-01 |title=The meaning of 'adiabatic' |url=http://www.nrcresearchpress.com/doi/10.1139/v94-121 |journal=Canadian Journal of Chemistry |language=en |volume=72 |issue=3 |pages=936–938 |doi=10.1139/v94-121 |issn=0008-4042}}</ref>

[[Quantum mechanics]] and [[quantum statistical mechanics]], however, use the word ''adiabatic'' [[Adiabatic theorem#Diabatic vs. adiabatic processes|in a very different sense]], one that can at times seem almost opposite to the classical thermodynamic sense. In quantum theory, the word ''adiabatic'' can mean something perhaps near [[Isentropic process|isentropic]], or perhaps near [[Quasistatic process|quasi-static]], but the usage of the word is very different between the two disciplines.

On the one hand, in quantum theory, if a perturbative element of compressive work is done almost infinitely slowly (that is to say quasi-statically), it is said to have been done ''adiabatically''. The idea is that the shapes of the eigenfunctions change slowly and continuously, so that no quantum jump is triggered, and the change is virtually reversible. While the occupation numbers are unchanged, nevertheless there is change in the energy levels of one-to-one corresponding, pre- and post-compression, eigenstates. Thus a perturbative element of work has been done without heat transfer and without introduction of random change within the system. For example, [[Max Born]] writes

{{quote|Actually, it is usually the 'adiabatic' case with which we have to do: i.e. the limiting case where the external force (or the reaction of the parts of the system on each other) acts very slowly. In this case, to a very high approximation

<math display="block">c_1^2=1,\,\,c_2^2=0,\,\,c_3^2=0,\,...\,,</math>

that is, there is no probability for a transition, and the system is in the initial state after cessation of the perturbation. Such a slow perturbation is therefore reversible, as it is classically.<ref>{{cite journal|last=Born |first=M. |author-link=Max Born |date=1927 |title=Physical aspects of quantum mechanics |journal=Nature |volume=119 |issue=2992 |pages=354–357|bibcode = 1927Natur.119..354B |doi = 10.1038/119354a0 |doi-access=free |translator-first=Robert |translator-last=Oppenheimer |translator-link=Robert Oppenheimer}}</ref>}}

On the other hand, in quantum theory, if a perturbative element of compressive work is done rapidly, it changes the occupation numbers and energies of the eigenstates in proportion to the [[Selection rule|transition moment integral]] and in accordance with [[time-dependent perturbation theory]], as well as perturbing the functional form of the eigenstates themselves. In that theory, such a rapid change is said not to be ''adiabatic'', and the contrary word ''diabatic'' is applied to it.

Recent research<ref>{{Cite journal |last1=Mandal |first1=Anirban |last2=Hunt |first2=Katharine L. C. |date=2020-03-14 |title=Variance of the energy of a quantum system in a time-dependent perturbation: Determination by nonadiabatic transition probabilities |journal=The Journal of Chemical Physics |volume=152 |issue=10 |pages=104110 |doi=10.1063/1.5140009 |pmid=32171229 |bibcode=2020JChPh.152j4110M |s2cid=212731108 |issn=0021-9606|doi-access=free }}</ref> suggests that the power absorbed from the perturbation corresponds to the rate of these non-adiabatic transitions. This corresponds to the classical process of energy transfer in the form of heat, but with the relative time scales reversed in the quantum case. Quantum adiabatic processes occur over relatively long time scales, while classical adiabatic processes occur over relatively short time scales. It should also be noted that the concept of 'heat' (in reference to the quantity of [[thermal energy]] transferred) breaks down at the quantum level, and the specific form of energy (typically electromagnetic) must be considered instead. The small or negligible absorption of energy from the perturbation in a quantum adiabatic process provides a good justification for identifying it as the quantum analogue of adiabatic processes in classical thermodynamics, and for the reuse of the term.

In classical thermodynamics, such a rapid change would still be called adiabatic because the system is adiabatically isolated, and there is no transfer of energy as heat. The strong irreversibility of the change, due to viscosity or other [[entropy production]], does not impinge on this classical usage.

Thus for a mass of gas, in macroscopic thermodynamics, words are so used that a compression is sometimes loosely or approximately said to be adiabatic if it is rapid enough to avoid significant heat transfer, even if the system is not adiabatically isolated. But in quantum statistical theory, a compression is not called adiabatic if it is rapid, even if the system is adiabatically isolated in the classical thermodynamic sense of the term. The words are used differently in the two disciplines, as stated just above.