"every force encountered in mechanics does not have an associated potential energy. for example work done by friction over a closed path is not zero and no potential energy can be associated with friction" explain these statements

Dear student ,
if the force is conservative then their will be associated potential energy . Because the concept of conservative force is the negative workdpne by conservative force is stored in the form of potential energy . While for non conservative force like friction their is no associated potential energy that's the property of force . The negative workdpne by these force is loss of mechanical energy in terms of heat . So this is the fundamental difference.