if the work for an applied force is independent of the path, then the work done by the force, by the gradient theorem, defines a potential function which is evaluated at the start and end of the trajectory of the point of application. this means that there is a potential function "u"(x), that can be evaluated at the two points x("t") and x("t") to obtain the work over any trajectory between these two points. it is tradition to define this function with a negative sign so that positive work is a reduction in the potential, that is