Learn English – “have a feeling that” vs. “have the feeling that”

The "zero article", otherwise known as simply not using an article, either indicates a proper name, or an abstract concept.

Apple is the most common fruit in the region.

This cannot be correct, because you are not talking about the abstract concept of an apple, but rather about a very real and concrete object.

Apple is the platonic ideal of fruit.

This example is closer to correct, because we are now talking about the concept of the apple, but even here, apple is simple to real and concrete to be usable with the zero article. This is also wrong.

Apple is on my mind.

Finally, we have come to a correct sentence, thoroughly converting a concrete noun into an abstract concept that I am merely thinking about. But even here, alone, without context, the idea of treating the word "apple" as an abstract concept is so strange that most people would reinterpret the sentence to treat "Apple" as a proper noun instead, especially since there exists a very real and well known company with the proper name of "Apple". But it does work, grammatically, the other way... it's just a very strange idea. You might find it in a philosophy textbook.

The is an article adjective. It implies a specific set of years. You could say

As years pass, white dwarfs cool down and begin to dim.

and be just as grammatically correct. But let's say in context it was phrased like this:

White dwarfs take several million year to implode. As the years pass, they cool down and begin to dim.

In this context, "the years" refers to the several million in the previous sentence. As I mentioned though, both the first and the second sentences you quoted are perfectly grammatically correct, but I find that "the years" is more commonly used.