We consider macroscopically large 3-partitions (A,B,C) of connected subsystems AUBUC in infinite quantum spin chains and study the Rényi-alpha tripartite information I(alpha)
3(A,B,C). At equilibrium in clean 1D systems with local Hamiltonians it generally vanishes. A notable exception is the ground state of conformal critical systems, in which I(alpha)
3(A,B,C) is known to be a universal function of the cross ratio x=|A||C|/[(|A|+|B|)(|C|+|B|)], where |A| denotes A's length. We identify different classes of states that, under time evolution with translationally invariant Hamiltonians, locally relax to states with a nonzero (Renyi) tripartite information, which furthermore exhibits a universal dependency on x. We report a numerical study of I(alpha)
3 in systems that are dual to free fermions, propose a field-theory description, and work out their asymptotic behavior for alpha=2 in general and for generic alpha in a subclass of systems. This allows us to infer the value of I(alpha)
3 in the scaling limit x→1−, which we call “residual tripartite information”. If nonzero, our analysis points to a universal residual value −log2 independently of the Renyi index alpha, and hence applies also to the genuine (von Neumann) tripartite information.
