(433b) Dynamical Processes in the Small-Numbers Limit

The dynamical laws, such as Fick's law of diffusion and Fourier's law of heat flow, apply to macroscopic systems. However, inside biological cells and in applications in nanotechnology, the numbers of particles is often small. Do the bulk dynamical laws apply to them? And, how can we explore the dynamical distribution functions? We have performed microfluidics experiments to test Fick's Law in the small numbers limit. We observe the distribution of particle fluxes, including those that have sometimes been called "2nd Law Violations" because they involve flows up a concentration gradient, rather than down it. We show that these dynamical fluctuational quantities are well-predicted by an approach called Maximum Caliber. This approach is similar to the Maximum Entropy approach of thermodynamics, but is applied to microtrajectories, rather than microstates, in order to account for the dynamics.