When Does Memory Matter?

When does memory fundamentally control the dynamics of complex systems, when can it be safely neglected, and how should it be incorporated into predictive reduced models when it cannot?

All systems we investigate are ultimately connected to their surroundings, and they often exhibit non-Markovian behavior, where future evolution depends not only on the present state but also on the system's history. A central challenge in modeling complex dynamical systems is therefore determining when memory effects must be retained in reduced descriptions and when they can be neglected without sacrificing predictive accuracy. What physical regimes make memory essential? When does the computational cost of retaining memory outweigh its predictive benefit? And what theoretical or algorithmic advances can change this balance?

Memory arises naturally across a wide range of theoretical frameworks. The Mori–Zwanzig formalism provides a unifying projection-operator perspective for deriving reduced dynamical equations in classical and quantum systems, leading to generalized Langevin equations and generalized master equations. Closely related time-nonlocal structures appear in nonequilibrium Green's function methods and embedding approaches, where interactions with unresolved degrees of freedom or an environment generate effective memory in the dynamics of the system of interest.

Different research communities, however, have developed distinct perspectives on when memory matters and how it should be treated. In biomolecular simulations, memory-aware reduced models can improve predictions of long-time conformational dynamics from short simulations. In open quantum systems and quantum materials, memory terms arise naturally in formal descriptions, while practical approximations often seek regimes in which they can be simplified or neglected. In condensed-matter and quantum many-body physics, memory is closely connected to relaxation, transport, and the emergence of effective dynamical descriptions. Meanwhile, applied mathematics provides increasingly powerful approaches for constructing, analyzing, and numerically solving reduced models with memory.

This workshop will bring these communities together around a common question: When does memory fundamentally control the dynamics of complex systems, when can it be safely truncated or replaced by an effective Markovian description, and how should it be incorporated into predictive models when it cannot? By bringing together researchers who often study closely related problems using different languages, approximations, and computational tools, we hope to identify common principles, clarify genuine differences across physical regimes, and stimulate new connections across disciplines.