I am studying basic mechanics and have reached the chapter on potential energy. However I am a bit confused about the difference between potential energy and the formula for the potential energy due to work done by a conservative force. I am not sure which of the following interpretations is correct:
One possibility is that potential energy is a general idea which doesn't have anything to do with conservative forces. The formula for potential energy however would only be for conservative forces, because the textbook says that the work done by nonconservative forces depends on the path and not just the end points, hence a formula for them doesn't exist.
So in this possibility, it would seem as though potential energy is one thing, and the formula for it is another (more specific) thing which only exists for conservative forces. But then why are both referred to as "potential energy", and why does the textbook say that potential energy is defined by the formula (meaning that potential energy as a general concept is specifically only for conservative forces?).
Another possibility is that potential energy is only defined for conservative forces to begin with. In this case, there would be no such thing as potential energy for nonconservative forces.
But this confuses me a bit because the book defines potential energy without reference to conservative forces, as simply being the energy a system possesses due to its configuration. However, the reason why I think possibility 2 is correct is because all of the textbooks I have read say that potential energy is defined by the formula for potential energy due to a conservative force. This would mean that potential energy indeed only exists for conservative forces.
I am unable to decide which of the two possibilities is correct. There seems to be a contradiction here which I am not seeing how to avoid.