Words that have absolute meanings at the end of a gradable scale (as in silence meaning an absolute absence of sound) are sometimes used to emphasise or exaggerate the extent of something, especially informally. If it is an exaggeration it won't be used literally, so won't be at the absolute extreme end of a scale, so could be used comparatively. If it is used for emphasis, a gradable descriptor may be added to make it even more emphatic.
A: It's totally silent in here!
B: Try going in the anechoic chamber, it's even more silent!
Some such words could also be considered a class in and of themselves, within which things can be graded. For example, take impossible. Out of two things that are impossible, it may be the case that one is conceptually harder to achieve than the other. In this circumstance, it makes some sense to grade the level of impossibility.
For example:
It's impossible to jump from the floor onto the roof of a house.
It's even more impossible to jump up to the top of the Eiffel Tower. (because it's taller)
Both actions are impossible, but one is conceptually more difficult to achieve than the other. Stating it as "more impossible" is a succinct way of stating this.
As you are probably aware, e.g. is an abbreviation of the Latin phrase exempli gratia, and means “for the sake of an example”. Technically, it should be followed by an example, i.e., by a single example. In reality, no-one has ever worried about this technicality, and it is not uncommon to find a list of examples following 'e.g.'.
There are many Latin words and phrases used in English, as well as words and phrases from many other foreign languages. When these word and phrases are used in English, it is not uncommon for native speakers to ignore the correct singular and plural distinctions that apply in the original language. E.g.
1/ English uses 'agenda' (singular) and 'agendas' (plural) instead of the Latin 'agendum' (singular) and 'agenda' (plural)
2/ English tends to just use 'graffiti' for singular and plural
instead of the Italian 'graffito' (singular) and 'graffiti' (plural).
A small percentage of English speakers will use these, and other foreign phrases, correctly (i.e., according to their language of origin), but most do not. The longer a foreign term has been adopted into English use, the more likely will its native grammar rules be ignored or forgotten.
As you can see above, I have used 'e.g.' with two examples, which I have numbered to make it obvious that I have done so. I have also seen people label a list of examples using e.g.1, e.g. 2, etc. But I would not recommend this unless it was mandated as the house style of a particular journal.
Best Answer
First off,
as little as possible
is the only option that I have ever read or used. I believe the other example you listed is grammatically correct, but it really isn't used.Second, your example sentence should read:
Energy for transportation from heat source to evaporator needs to be used as little as possible.
The term means basically, while you may need to use some energy you should try to use the least amount that you can function with.
Other uses would be:
The hotel did as little as possible to make me comfortable! They only gave me one towel, and there wasn't even a coffee machine