Because work done against friction depends on path length, why is there no potential energy function associated with a nonconservative force like friction?

1. A potential energy function assigns a single value to each position, which only works if the associated force's work depends solely on starting and ending points. 2. Friction's work instead depends on the length of the path taken, so no single position-based potential energy value could correctly capture it. 3. This has nothing to do with the size of the friction force or whether the object is moving, since even large or small friction forces are equally path dependent. 4. Potential energy is defined for any conservative force, not gravity alone, as shown earlier by the spring's potential energy, so the real reason is the path dependence of friction's work. _Source: OpenStax College Physics (CC BY 4.0), Ch 7 "Work, Energy, and Energy Resources", section 7.5 Nonconservative Forces_