A Statistical Mechanics Perspective on Memory and Forgetting in Nonequilibrated Polymer Films

Polymer systems prepared far from equilibrium often retain long-lived memory of their processing history, manifested experimentally as molecular recoiling stresses and their anomalous relaxation behavior. Relaxation may therefore be viewed as the gradual erasure of stored nonequilibrium memory (forgetting). Experiments on spin-coated polymer thin films reveal relaxation behavior that lies beyond the scope of conventional equilibrium polymer dynamics and continuum viscoelastic descriptions, which only partially explain it. Yet a unifying statistical-mechanical framework for these observations has remained elusive. In this Perspective, I argue that such phenomena can be understood as the non-Markovian regression of constrained conformational entropy. Pivoting from Onsager’s regression hypothesis, the theory of dynamics of nonequilibrium variables, and the Mori–Zwanzig projection-operator formalism, molecular recoiling stress is identified as a slow nonequilibrium variable governing relaxation in nonequilibrated polymer systems. Projecting the microscopic dynamics onto this variable leads naturally to a stress-projected generalized Langevin equation with a history-dependent memory kernel. This minimal coarse-grained description accounts for stretched-exponential stress relaxation, Arrhenius temperature dependence, and the experimentally observed scaling of relaxation times with polymer chain length. The aim is not to introduce new microscopic models, but to provide a simple and general statistical-mechanics framework that rationalizes history-dependent stress relaxation in polymers and clarifies how polymers gradually forget their preparation history far from equilibrium. More broadly, this framework suggests that polymer memory and slow relaxation arise from the regression of constrained conformational entropy stored during nonequilibrium preparation, with topological constraints acting on nonequilibrium polymer ensembles to generate persistent, history-dependent mechanical responses.