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In living systems, collective molecular behavior is driven by thermodynamic forces in the form of chemical gradients. Leveraging recent advances in the field of nonequilibrium physics, I show that increasing the thermodynamic force alone can induce qualitatively new behavior. To demonstrate this principle, general equations governing kinetic proofreading and microtubule assembly are derived. These equations show that new capabilities, including catalytic regulation of steady-state behavior and exponential enhancement of molecular discrimination, are only possible if the system is driven sufficiently far from equilibrium, and can emerge sharply at a threshold force. Regardless of design parameters, these results reveal that the thermodynamic force sets fundamental performance limits on tuning sensitivity, error, and waste. Experimental data show that these biomolecular processes operate at the limits allowed by theory.