Week 17.02.2025 – 23.02.2025

The dynamics of many-body systems, such as gases of particles or lattices of spins, often display, at large scales of space and time, a high degree of universality. Indeed, this dynamics is usually described by a few equations, those of hydrodynamics, representing
the flows of conserved currents such as those of particles and energy. This is because other "degrees of freedom" thermalise much more quickly, and the full dynamics projects onto that of conserved currents. In fact, surprisingly, even correlations between
local observables at large separations in time, and large-scale fluctuations, can be described by hydrodynamics. This is the object of various theories of hydrodynamic fluctuations, such as macroscopic fluctuation theory (for systems where diffusion dominates),
and its ballistic counterpart (for systems where persistent currents exist). I will introduce the main ideas behind such theories, restricting to systems in one dimension of space for simplicity. I will concentrate on perhaps the simplest and newest, ballistic
macroscopic fluctuation theory, taking simple examples such as the gas of classical hard rods (hard spheres, but in one dimension) - but many concepts are general.

How does a biological system produce long time scales that vastly outlast intrinsic biochemical rates, yet are not infinite? This challenge features in various biological tasks involving memory and sensing. We uncover how this also manifests in the cellular assembly of a C. elegans embryo. High-resolution imaging reveals that the formation of the cell’s actin cortex is preceded by a stage where thousands of highly branched actin structures transiently grow and disassemble [1]. Many structures grow orders of magnitude past intrinsic degradation time scales before disassembling, yet without proliferating. We uncover how an overlooked bifurcation in the underlying biochemical dynamics can account for this huge lifetime disparity. We find that a simple mechanism based on resource competition can guide the system towards this dynamical bifurcation without the need for parameter fine-tuning or a biological regulatory mechanism. If time allows I will mention

[1] Victoria Tianjing Yan, Arjun Narayanan, Tina Wiegand, Frank Jülicher, Stephan W. Grill, Nature (2022).