Potential and momentum together then define the state of the particle. This allows to treat thermodynamic systems consisting of many particles, where individual coordinates loose significance and average values describing the system take precedence.
Lets consider the free energy as a first example.
A change of state thus necessarily demands a change in at least one of the three generalized coordinates from the above example. This can be understood as a generalized force . If the derivative happens to be taken with respect to a space coordinate of the system, the generalized force is a real mechanical force - it describes the change of energy with space as it should. You have to resort to physical or mathematical reasoning to find out. 2 - W 1 thus are not independent of the path, therefore they are not state functions and their differentials cannot be total differentials Now lets turn to mathematical reasoning.