Hidden Phase Transition in Single-Polymer Stretching under Elongational Flow

Using machine learning, we identify a second transition in polymer chain stretching driven by planar elongational flow, beyond the well-known coil-stretch transition. We achieve this by developing a conditional extension of Universal and Identifiable Dissipative Dynamics (UIDD) that jointly learns reduced stochastic dynamics from microscopic trajectories across flow strengths and yields the corresponding stationary nonequilibrium free energy landscapes. As the flow strength increases, the evolving landscape exhibits the expected coil-stretch transition, and then a previously unrecognized dynamical transition. In the latter, the stretched states persist, but the distribution along a folding coordinate becomes bimodal when conditioned on small end-to-end separation. Large-deviation analysis of a simplified analytical chain model reproduces both transitions and shows that they are phase transitions in the long-chain limit. Single-molecule DNA experiments provide qualitative support for the dynamical transition through the predicted reversal of the folding response.