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The notion of an adiabatic process in thermodynamics -vs- quantum mechanics

+ 7 like - 0 dislike
132 views

I'm confused about the terminology in the two contexts since I can't figure out if they have a similar motivation. Afaik, the definitions state that quantum processes should be very slow to be called adiabatic while adiabatic thermodynamic processes are supposed to be those that don't lose heat. Based on my current intuition, this would mean that the thermodynamic process is typically fast (not leaving enough time for heat transfer). What gives, why the apparent mismatch?

This post imported from StackExchange Physics at 2014-04-24 02:36 (UCT), posted by SE-user Siva
asked Apr 24, 2013 in Theoretical Physics by Siva (710 points) [ no revision ]

3 Answers

+ 4 like - 0 dislike

The terminological mismatch arises because different physicists use the terms differently in different contexts. For example, here is how Landau and Lifshitz define an adiabatic process in the context of thermodynamics:

Let us suppose that a body is thermally isolated, and is subject to external conditions which vary sufficiently slowly. Such a process is said to be adiabatic

As you can see, these authors combine the criterion of thermal isolation (no heat exchange with the environment) with a slowness assumption, to arrive at their definition of the term adiabatic. In contrast, consider Huang's definition of adiabatic in the context of thermodynamics;

Any transformation the system can undergo in thermal isolation is said to take place adiabatically.

In the context of quantum mechanics, Griffiths defines the term adiabatic as follows:

This gradual change in external conditions characterizes as adiabatic process.

I would say, from personal experience, that the more widely held convention for the term adiabatic is not the one used by Landau and Lifshitz. In particular, most physicists I know use the term adiabatic in the context of thermodynamics to mean thermally isolated, while they use the term adiabatic in the context of quantum mechanics to mean sufficiently slow that certain approximations can be made.

Addendum. In the context of thermodynamics, the free expansion of a thermally isolated ideal gas is often referred to as an "adiabatic free expansion of a gas," see, for example here. Such a process is not isentropic. Using Slavik's definition would deem invalid the characterization of such a free expansion as adiabatic. However, all you need to do is google "adiabatic free expansion" to see how widespread such use of the terminology is.

People can make all of the unqualified, seemingly confident statements about what the term "adiabatic" means, but it's simply false that everyone uses the same definition, and I think its unproductive to call widely used conventions other than your own "not sensible."

This post imported from StackExchange Physics at 2014-04-24 02:36 (UCT), posted by SE-user joshphysics
answered Apr 24, 2013 by joshphysics (830 points) [ no revision ]
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With all due respect, I disagree. Explosion in a thermally isolated box is not adiabatic by any sensible definition. So it is not only the isolation - I explain myself more in a separate answer.

This post imported from StackExchange Physics at 2014-04-24 02:36 (UCT), posted by SE-user Slaviks
@Slaviks What exactly are you disagreeing with? My statements pertain only to what I perceive to be a widely held convention about how a term is defined. Are you saying that you think using adiabatic as a synonym for thermally isolated is not a common convention? I'm certain that I can site multiple sources to show that there are a sizable number of physicists who use the term in that way.

This post imported from StackExchange Physics at 2014-04-24 02:36 (UCT), posted by SE-user joshphysics
We apparently disagree only on matters of taste - I just disapprove, and hence downvote, the convention of identifying adiabatic with thermally isolated (even if the convention is commonly held). Sorry if it is too harsh by the community standards here.

This post imported from StackExchange Physics at 2014-04-24 02:36 (UCT), posted by SE-user Slaviks
@Slaviks I respect your opinion and downvote; I just want to make the issue clear for future readers so that they can make decisions on matters of taste for themselves. I also don't think you're being harsh at all; I hope you continue to be authentic in your assessments of respones.

This post imported from StackExchange Physics at 2014-04-24 02:36 (UCT), posted by SE-user joshphysics
@joshpysics I am happy we agree to disagree! It should be good for the readers to see different perspectives and judge for themselves.

This post imported from StackExchange Physics at 2014-04-24 02:36 (UCT), posted by SE-user Slaviks
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I agree with @joshphysics. In chemistry it is unambiguous that "adiabatic" means "thermally isolated". Thus an explosion, at least in its initial stages, can be and is treated as adiabatic because there is not enough time to exchange much heat with the surroundings. Further, adiabatic processes do NOT have to be at or near equilibrium. Those paths are called "reversible". Adiabatic paths can be reversible but are not mandated to be such.

This post imported from StackExchange Physics at 2014-04-24 02:36 (UCT), posted by SE-user Paul J. Gans
My encounters with the terminology have been the same as @joshphysics describes. The point of my question was to understand if there's a common underlying theme to the (seemingly) disparate conventions.

This post imported from StackExchange Physics at 2014-04-24 02:36 (UCT), posted by SE-user Siva
+ 3 like - 0 dislike

Adiabatic means quasi-static and isoentropic - slow enough to create negligible amount of irreversible excitation. This is the common rationale of technically different definitions. E.g., Landau & Lifshic'es definition has two components - thermally isolated (to prevent entropy change by heat exchange) and slow (to prevent irreversible excitation). For a gaped quantum system adiabatic can by quite fast (just keep Planck constant times the characteristic driving rate below the value of the energy gap).

What is confusing indeed is that there can be an intermediate speed which you can be reasonably adiabatic - much faster than heat exchange with what you separate as the "reservior" but much slower than the equilibraton speed of the degrees of freedom being excited. That's why adiabatic can be fast and slow at the same time - there are two conditions to satisfy. These subtleties are often not made sufficiently clear,
but that's what we have physics.SE for :)

To sum up, don't make "waves" (entropy) and you'll adiabatic.

This post imported from StackExchange Physics at 2014-04-24 02:36 (UCT), posted by SE-user Slaviks
answered Apr 24, 2013 by Slaviks (610 points) [ no revision ]
This sentence made me quite scared of life for a moment: "Adiabatic means quasi-static and isoentropic"

This post imported from StackExchange Physics at 2014-04-24 02:36 (UCT), posted by SE-user Magpie
That's good - life is not adiabatic! :)

This post imported from StackExchange Physics at 2014-04-24 02:36 (UCT), posted by SE-user Slaviks
I see what you did there ;)

This post imported from StackExchange Physics at 2014-04-24 02:36 (UCT), posted by SE-user Magpie
If I understand correctly, the adiabatic time scale being slower than the equilibration time scale implies that the process will be quasi-static, and hence reversible. We need it to be slower than the heat-transfer ("thermalization"?) time scale.

This post imported from StackExchange Physics at 2014-04-24 02:36 (UCT), posted by SE-user Siva
In QM, all processes are reversible, so presumably we don't need the notion of quasi-static (which knocks off the smallest time scale). So I would naively think that the adiabatic condition you phrased in terms of the energy gap should give an upper limit on the time scale (to replace the notion of no heat transfer), but it seems to serve as a lower limit. That confuses me.

This post imported from StackExchange Physics at 2014-04-24 02:36 (UCT), posted by SE-user Siva
+ 2 like - 0 dislike

The etymology of adiabatic appears to be from the Greek meaning "not passable" (native Greek speakers should feel free to clarify and/or correct that). In the technical meanings, the "passing" refers to heat transfer. So in thermodynamics, adiabatic means there is no heat transfer between the system and the environment.

In practice, of course, that's an approximation. In practice, adiabatic means that the thermodynamic process is slow enough that the system is always very nearly in equilibrium, so the heat exchange with the environment is negligible. In quantum mechanics, the analog to equilibrium is an eigenstate. So adiabatic means that the change is so slow that the system is always very nearly in equilibrium, so the system is always in an eigenstate. Both of these are approximations.

In quantum mechanics, the opposite of the adiabatic approximation is the sudden approximation. Take a system with initial Hamiltonian $H_0$, and change the Hamiltonian to $H_1$ over some time $T$. Then the adiabatic approximation is $T \rightarrow \infty$, and the sudden approximation is $T \rightarrow 0$. In the sudden approximation, the state of the system doesn't change (it "doesn't have time to change"), and it finds itself suddenly not in an eigenstate. In the adiabatic approximation, the state follows the perturbation, and is always in an eigenstate of the Hamiltonian.

This post imported from StackExchange Physics at 2014-04-24 02:36 (UCT), posted by SE-user Colin McFaul
answered Apr 24, 2013 by Colin McFaul (60 points) [ no revision ]
"In quantum mechanics, the analog to heat exchange with the environment is the system changing state." Could you please elaborate on that?

This post imported from StackExchange Physics at 2014-04-24 02:36 (UCT), posted by SE-user Siva
@Siva, I've added a paragraph in response to your comment. Thanks for that, as my original answer was a bit imprecise and incorrect.

This post imported from StackExchange Physics at 2014-04-24 02:36 (UCT), posted by SE-user Colin McFaul

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