  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, surprisingly, the entropy production rate is maximized in
the non-contractile, stable state. Our study provides evidence that the origins
of system entropy production and activity-dependent dissipation arise from
disorder in the molecular interactions between actin and myosin
