In the framework of irreversible thermodynamics, we study the transport properties of hot quark-gluon plasmas. The viscous entropy production at finite chemical potential as well as the shear viscosity to non-equilibrium entropy density ratio is investigated in weakly coupled limit by using kinetic theory. The results show that the chemical potential contributes positively to their ratio compared to the pure temperature case. The ratio exhibits two boundaries in the coupling strength in which a minimum value of 0.42 is found at αs = 0.6.