We examine the mean relaxation time predicted by the Maxwell relation for stress and structural alpha-relaxation phenomena. We express this relation using the Markov network framework and present an expression for the average relaxation time under equilibrium and nonequilibrium conditions that is rooted in the energy landscape of a material. We show that structural relaxation times calculated using the Maxwell relation must systematically underpredict the relaxation time. Finally, we report experimental evidence suggesting that the relaxation time obtained from shear viscosity measurements must correspond to a stress relaxation time.