Living systems consist of an enormous number of heterogeneous components, typically out-of equilibrium, and interacting among themselves as well as with an environment. At the same time, in many biological examples, including gene expression, neural activity and animal behavior, the analysis of experimental data has revealed the importance of low-dimensional modes. Conceptually, systems with high or low dimensionality suggest fundamentally different perspectives. Nonlinear dynamics frames complex systems in terms of low-dimensional governing differential equations that give rise to invariant properties, such as dynamical manifolds and their effective dimensionality. In contrast, high-dimensional approaches such as stochastic thermodynamics characterize these systems with a full description of microscopic rates, which requires more variables. Stochastic approaches also include tools such as coarse-grainings and concepts like entropy production rates or computational complexity. Recent years have seen rapid parallel advances of both approaches, often inspired by work close to biological data.
How should we bridge these pictures? This is an important problem both for the scientific characterization of the physics of living systems, but also fundamentally because the systems themselves may leverage dimensionality differently depending on their required function. For example, control is best achieved with a low-dimensional system, but adaptation or learning is likely to incorporate the fluctuations. In addition, it is unclear when lossy measurements of a stochastic system – that yield a low dimensional, nonlinear dynamics description – match a description that arises from a coarse-graining of the stochastic process.
Our proposed working group unites researchers with expertise in nonlinear dynamical systems and stochastic processes. Our discussions will explore novel principles of coarse graining that result in low-dimensional dynamics, but also how information can flow (in both directions) between these dynamics and the high-dimensional fluctuations. We will also seek relevant conceptual variables and frameworks. We anticipate that our working group will result in a perspective article in the shorter-term and new sustained collaborations in the longer-term.