Earlier in the year we said that the work necessary for hiking up the slope of Rampina Mountain vs. climbing straight up the cliff route would be the same, independent of the path taken.
This statement is true if you disregard friction and other factors, but one path has a greater length and more friction will be experienced (probably).
May approaches in physics are approximations, but they can be fairly accurate up to a certain point.
If you climb a rope, the friction between your hands and the rope or your gloves and the rope would be unique. The friction between your shoes and the ground could vary on shoe type, etc.
Or the ground could be icy……
Thus the work is not really path independent.
Even more so, thermodynamics is not path independent-
While throwing a marble up and watching it come down is symmetrical in motion, the rewinding of a camera of a thermodynamic reaction would definitely not be the same as playing it from the beginning (at least in all likeliness).