The adverbial yet stands at the junction of past and future, expressing the persistence of action in time:
...used as an adverb, yet defines an action's persistence in time. The
word can define an action in the past, present or future:
The first example from Wikipedia is persistence through the past into the present with implications of the future. Examining my past performance I have never been late, and that past performance offers an implicit promise of the future.
The second example is persistence in the present with implications of the past. I am still standing, but the larger context indicates that the past circumstances have not necessarily been favorable.
The third example is persistence in the future with implications of past and present. Through the past and up to the present, I have not arrived, but I will eventually arrive in the future.
The polarity behavior of yet requires a specific licensing context, which is a pivot between negative and positive polarity. Toward the past yet tends to be a negative polarity item, but it tends to pivot into a positive polarity item toward the future. This polarity pivot can happen in the present, depending on its connection to the context of past and future. Examining the Wikipedia examples:
- I have never yet been late expresses negative polarity in the past and in the present--I have never been late and implies a pivot to positive polarity toward the future--[I will continue that performance].
- I yet stand implies negative polarity toward the past--[Against implied opposition]--and expresses a pivot to positive
polarity in the present--I stand.
- I will yet arrive implies negative polarity toward the past and in the present--[Though I have not arrived], and expresses a pivot to
positive polarity toward the future--I will arrive.
Examining the polarity of yet in definitions at Oxford Dictionaries Online:
1.0 Up until the present or a specified or implied time; by now or then:
I haven’t told anyone else yet
aren’t you ready to go yet?
I have yet to be convinced
The expressed polarity toward the past is consistently negative, and a pivot to positive polarity toward the future is consistently expressed or implied, while the polarity in the present is determined by its connection to past and future.
- I haven't told anyone, [but I may tell someone in the future].
- You may not be ready to go yet, [but you may be ready in the future].
- [I am not convinced], but may be convinced in the future
[WITH SUPERLATIVE]: the congress was widely acclaimed as the best yet
Within the historical perspective of the statement, the comparison of the "current" congress to those of the past creates a negative polarity toward the past and pivots to positive polarity in the present.
- [Other congresses were not as good], but this one is the best.
1.1 [WITH NEGATIVE] As soon as the present or a specified or implied time:
wait, don’t go yet
The polarity in the present is expressed as negative, while the pivot to a positive polarity toward the future is implied--[you may go in the future].
I hope to continue for some time yet
An negative polarity in the present is implied--[there are forces that might oppose my hope] and yet pivots to a positive polarity toward the future.
1.3 Referring to something that will or may happen in the future:
further research may yet explain the enigma
I know she’s alive and I’ll find her yet
The polarity toward the past or in the present is implied as negative--[past research has not explained the enigma]...[there may be reasons to believe she is dead], and yet pivots to positive polarity toward the future.
2.0 Still; even (used to emphasize increase or repetition):
snow, snow, and yet more snow
yet another diet book
the rations were reduced
3.0 In spite of that; nevertheless: every week she gets worse, and yet it could go on for years
The positive-negative comparisons create a pivot, extending the normal licensing context for yet.
Examining the examples of the OP:
- A: We've got to hurry! B: Oh, calm down. It's early yet.
The context implies a negative polarity in the present rush and pivots to a positive polarity toward the future.
- A: Is he coming back soon? Has he finished his job in Beijing? B: No, he has two years yet.
No creates a negative polarity in the present time frame, and yet pivots into a positive polarity toward the future--he will come back after two years.
- We have a long time yet. We still can go to the gym.
The context implies a negative polarity in the present time frame--[we don't need to go to the gym now], and yet pivots into a positive polarity toward the future--we can go to the gym sometime in the future.
- We are only thirty minutes into the work yet. But I'm already tired.
Only creates a negative polarity toward the past and the conjunction but extends the negative polarity in the present, but the necessary pivot into a positive polarity is missing. The pivot would have been expressed by yet as a conjunction, if the sentence had been written:
We are only thirty minutes into the work, yet I'm already tired .
In the OP, the fourth example is not idiomatic--even thought the definitions fit-- because the context defies the licensing context for yet, which expresses or implies a pivot in polarity between past, present and future.