Significance: Proteins capable of separating into three-dimensional liquid droplets in the cytoplasm and nuclei of cells sometimes assemble in a two-dimensional form at membranes. These surface densities, enriched in specific proteins and lipids, often play decisive roles in cell signaling and membrane organization. Here a theoretical approach suggests that surface densities resemble prewet surface phases held together through a combination of two-dimensional membrane-mediated forces and three-dimensional protein interactions. The emergent physics of these liquid surface phases enable their roles both as dynamic scaffolds and as cooperative switches that propagate signals between the membrane and bulk.

Significance: Most physical theories are effective theories, descriptions at the scale visible to our experiments which ignore microscopic details. Seeking general ways to motivate such theories, we find an information theory perspective: If we select the model which can learn as much information as possible from the data, then we are naturally led to a simpler model, by a path independent of concerns about overfitting. This is encoded as a Bayesian prior which is nonzero only on a subspace of the original parameter space. We differ from earlier prior selection work by not considering an infinite quantity of data. Having finite data is always a limit on the resolution of an experiment, and in our framework this selects how complicated a theory is appropriate.

Complex models in physics, biology, economics, and engineering are often sloppy, meaning that the model parameters are not well determined by the model predictions for collective behavior. Many parameter combinations can vary over decades without significant changes in the predictions. This review uses information geometry to explore sloppiness and its deep relation to emergent theories. We introduce the model manifold of predictions, whose coordinates are the model parameters. Its hyperribbon structure explains why only a few parameter combinations matter for the behavior. We review recent rigorous results that connect the hierarchy of hyperribbon widths to approximation theory, and to the smoothness of model predictions under changes of the control variables. We discuss recent geodesic methods to find simpler models on nearby boundaries of the model manifold—emergent theories with fewer parameters that explain the behavior equally well. We discuss a Bayesian prior which optimizes the mutual information between model parameters and experimental data, naturally favoring points on the emergent boundary theories and thus simpler models. We introduce a ‘projected maximum likelihood’ prior that efficiently approximates this optimal prior, and contrast both to the poor behavior of the traditional Jeffreys prior. We discuss the way the renormalization group coarse-graining in statistical mechanics introduces a flow of the model manifold, and connect stiff and sloppy directions along the model manifold with relevant and irrelevant eigendirections of the renormalization group. Finally, we discuss recently developed ‘intensive’ embedding methods, allowing one to visualize the predictions of arbitrary probabilistic models as low-dimensional projections of an isometric embedding, and illustrate our method by generating the model manifold of the Ising model.

Living and non-living active matter consumes energy at the microscopic scale to drive emergent, macroscopic behavior including traveling waves and coherent oscillations. Recent work has characterized non-equilibrium systems by their total energy dissipation, but little has been said about how dissipation manifests in distinct spatiotemporal patterns. We introduce a measure of irreversibility we term the entropy production factor to quantify how time reversal symmetry is broken in field theories across scales. We use this scalar, dimensionless function to characterize a dynamical phase transition in simulations of the Brusselator, a prototypical biochemically motivated non-linear oscillator. We measure the total energetic cost of establishing synchronized biochemical oscillations while simultaneously quantifying the distribution of irreversibility across spatiotemporal frequencies.

Many biological processes require timely communication between molecular components. Cells employ diverse physical channels to this end, transmitting information through diffusion, electrical depolarization, and mechanical waves among other strategies. Here we bound the energetic cost of transmitting information through these physical channels, in $k_{B}T/\mathrm{bit}$, as a function of the size of the sender and receiver, their spatial separation, and the communication latency. These calculations provide an estimate for the energy costs associated with information processing arising from the physical constraints of the cellular environment, which we find to be many orders of magnitude larger than unity in natural units. From these calculations, we construct a phase diagram indicating where each strategy is most efficient. Our results suggest that intracellular information transfer may constitute a substantial energetic cost. This provides a new tool for understanding tradeoffs in cellular network function.