Physical Chemistry Seminar: Universal Scaling Laws as Probes: From Diffusion to Natural Selection

Abstract:

How much can we learn about a system from its long-time dynamics? In this talk, I will show how scale-free relaxation can reveal otherwise inaccessible properties in two seemingly unrelated settings: local measurements and natural selection. In dilute systems with diffusive large-scale dynamics, a systematic analytical calculation predicts that the autocorrelation of local measurements decays as a universal power law, with a prefactor determined solely by density and effective diffusivity. Supported by simulations at and far from equilibrium, this law provides a route for techniques such as fluorescence correlation spectroscopy and dynamic light scattering to measure diffusivity even when microscopic motion is nondiffusive, as in active particles.

Interestingly, the Fourier-space integral underlying this law is mathematically analogous to the partition function governing natural selection after catastrophe. There, when selection acts on abundant existing variation, the gap between average and highest fitness shrinks inversely with time, with a prefactor proportional to the number of traits under selection. This law is a dynamical analog of the equipartition principle in statistical mechanics, allowing us to count effective trait axes in two experimental E. coli fitness landscapes, just as calorimetry counts the number of thermally excited degrees of freedom in a gas. Together, these laws provide quantitative probes of underlying structures, from diffusive relaxation spectra to fitness-landscape geometry.

Seminar Organizer: Dr. Anael Ben Asher