Relational Closure Law and Second-Order Blindness in Non-Equilibrium Physics

A physical description can measure individual physical quantities correctly and still be incomplete because the missing information resides in relationships among those quantities. The Relational Closure Law states that physical sufficiency cannot be determined consistently from measured quantities alone; the description must include the minimum relational order required by the system. It is not an improved estimator, hidden-state reconstruction or statistical closure procedure, but a proposed cross-domain physical law governing physical sufficiency. The Law is tested through direct measurements of relational closure, closure order and target-blind prediction across physically distinct nonequilibrium systems. These tests uncover results that were not reported in the original studies. When checked against established physical and mathematical relations, those results pass at the stated resolution. RCL also reveals second-order blindness: covariance can vanish even though the underlying dependence remains maximal. Three driven rotary experiments realize finite blind states. Brownian-ring, Markov-cycle and quantum Otto classes establish the stronger result: the covariance null can persist while entropy production becomes arbitrarily large. Together, the results show that physical sufficiency can require a higher relational order and establish a fundamental limit on inference from covariance alone in nonequilibrium physics.