Master Work Function

The convergence of human cognition and automated processes in modern work calls for a unified theoretical framework to quantify meaningful work in hybrid human–machine systems. We introduce the Master Work Function (Φ), a scalar potential over socio‑technical state space whose differences bound the net meaningful work obtainable by a combined system of automated processes (A) and human processes (H). Leveraging the Jarzynski equality, cumulant‑generating functions, and gradient analysis, we prove that Φ is bounded in single‑sector limits (A = 0 or H = 0) yet unbounded under synergistic coupling, and we derive design rules for optimal task allocation. Applications span collaborative robotics, cyber‑physical infrastructure, AI value alignment, education, and future‑of‑work economics. Philosophical implications for agency, dignity, and technology‑mediated human flourishing are discussed.