Mechanical organization yields degenerate dissipation beyond linear response

Abstract

In non-equilibrium (active) systems, increased driving is commonly assumed to produce proportionally greater energy dissipation. Using picowatt-sensitive calorimetry, entropy-production analysis, rheology, and microscopy in reconstituted actomyosin networks, we show that this relationship breaks down as the material reorganizes under motor activity. Dissipation initially increases with myosin abundance but subsequently decreases despite continued network stiffening, indicating that energetic cost becomes regulated by the evolving mechanical state rather than actuator abundance alone. Comparing catch-bond (-actinin) and slip-bond (fascin) crosslinked networks reveals that bond mechanics shift the critical motor concentration at which this transition occurs, marking the onset of state-dependent energy conversion. Although these networks generate distinct active stresses and mechanical states, they can exhibit comparable dissipation rates, revealing that state-dependent energy conversion can produce degenerate dissipation, whereby mechanically distinct states exhibit similar energetic costs. These findings demonstrate that dissipation in active materials is governed not only by the magnitude of driving but also by the mechanical state that emerges in response to that driving, providing an experimental example of state-dependent energy conversion far from equilibrium.