The actin cytoskeleton is an active semi-flexible polymer network whose non-equilibrium properties coordinate both stable and contractile behaviors to maintain or change cell shape. While myosin motors drive the actin cytoskeleton out-of-equilibrium, the role of myosin-driven active stresses in the accumulation and dissipation of mechanical energy is unclear. To investigate this, we synthesize an actomyosin material in vitro whose active stress content can tune the network from stable to contractile. Each increment in activity determines a characteristic spectrum of actin filament fluctuations which is used to calculate the total mechanical work and the production of entropy in the material. We find that the balance of work and entropy does not increase monotonically and the entropy production rate is maximized in the non-contractile, stable state of actomyosin. Our study provides evidence that the origins of entropy production and activity-dependent dissipation relate to disorder in the molecular interactions between actin and myosin.