Information-driven transitions in projections of underdamped dynamics

Abstract

Low-dimensional representations of underdamped systems often provide insightful grasps and analytical tractability. Here, we build such representations via information projections, obtaining an optimal model that captures the most information on observed spatial trajectories. We show that, in paradigmatic systems, the minimization of the information loss drives the appearance of a discontinuous transition in the optimal model parameters. Our results raise serious warnings for general inference approaches and unravel fundamental properties of effective dynamical representations, impacting several fields, from biophysics to dimensionality reduction.

Mutual information in changing environments: non-linear interactions, out-of-equilibrium systems, and continuously-varying diffusivities

“…Recently, we showed that the mutual information of systems with linear interactions and a switching discrete-state environment receive disentangled contributions from environmental and internal interactions [13]. This result revealed that the properties of the information content of complex systems can be particularly informative, and that tools from information theory may greatly help to capture their essential features [14].…”