A classical, deterministic chaotic system whose state an observer can only estimate probabilistically exhibits a phase transition governed by how precisely it is repeatedly measured. By mapping Bayesian state estimation on a branching tree onto a directed polymer, the growth rate of the observer's Shannon entropy switches from a reduced-Lyapunov chaotic regime to a bounded strong-measurement regime, with a universal scaling function at the critical point that coincides with the directed polymer's freezing transition.
A solvable statistical-physics model of a measurement-induced phase transition (MIPT) in a purely classical, deterministic chaotic system. An observer who knows a chaotic trajectory only probabilisti…