Informational Viscosity as a Finite-Memory Closure for Driven 1D Anyons

Cold-atom experiments now control the exchange phase of strongly interacting one-dimensional gases and resolve the asymmetric momentum distribution of a driven impurity together with its relaxation after trap release. We introduce a finite-memory closure from Viscous Time Theory (VTT) for the preparation-history dependence of this observable. The prepared exchange phase remains the experimental control variable; a causal reduced coordinate follows it with a finite response time, and the mismatch between the two is the VTT state variable. Under an odd-response condition on the impurity momentum distribution, the momentum skewness acquires a linear, history-resolved correction. We test the closure in a microscopic reference model, a spinful Bose–Hubbard ring with exact time evolution, using protocols that end at the same exchange phase and differ only in their history. Interacting systems develop a history-dependent skewness that is small and oscillatory for slow preparation and of order one for fast preparation. An oscillatory generalization of the closure, calibrated on monotonic ramps alone and then frozen, predicts the held-out reversal protocols and reduces the mean-square error of the memoryless adiabatic baseline in the slow regime by 30 to 45% at fixed interaction strength and by 12% after averaging over a 20% spread of interaction strength. The response persists at a larger system size, where its frequency follows the lower level spacing of the system. The results define a quantitative experimental programme: calibrate on monotonic pulses, predict reversal pulses, and compare with a full microscopic baseline supplied with the same pulse history.