Cellular adaptation operates far from equilibrium. It is governed by the nonequilibrium driving force. Yet how these nonequilibrium dynamics quantitatively determine the trade-offs among speed, robustness and cost remains unclear. Using the yeast pheromone response as a model system, we develop a unified framework linking adaptation kinetics, nonequilibrium characteristics, and landscape topology. Our analysis reveals synchronized biphasic responses across these domains, marked by landscape flattening, pathway convergence, and elevated thermodynamic dissipation. Across the pheromone-dose crossover, the system shifts from fast, distributed adaptation with reduced dissipation to slow, robust dynamics stabilized by dominant pathways. By integrating dynamics with thermodynamics, this framework quantifies the thermodynamic and topological constraints of cellular decision-making, providing a generalizable strategy for dissecting adaptation across complex biological systems.