Mark Mineev, Simons Center for Geometry & Physics, Stony Brook University

"Stochastic Laplacian growth of air bubbles in a viscous fluid"

Abstract: A point source on a plane constantly emits particles which diffuse until they stick to a growing cluster. The cluster growth probability is given by a sum over all possible scenarios leading to the same final shape. The most probable scenario reproduces the Laplacian growth equation. Strikingly, the entropy increment is the electrostatic energy of a charged layer grown during the time step. Hence the growth probability of the nonequilibrium process obeys the equilibrium Gibbs-Boltzmann statistics. The results are related to the Onsager minimal dissipation principle and minimum entropy production that Prigogene proposed for from equilibrium equilibria.