Stochastic Laplacian growth and unresolved selection puzzles
JAN 19, 2018 | 11:00 AM TO 1:30 PM
The Graduate Center
365 Fifth Avenue
January 19, 2018: 11:00 AM-1:30 PM
Initiative for the Theoretical Sciences and Ph.D Program in Physics
Mark Mineeve-Weinstein (SCGP, Stony Brook)
A point source on a plane constantly emits particles which rapidly diffuse until they stick to a growing cluster. The growth probability of a cluster is presented as a sum over all possible scenarios leading to the same final shape. The most probable scenario and reproduces the Laplacian growth equation, which embraces numerous fundamental free boundary dynamics in non-equilibrium physics.
Strikingly, the entropy increment is shown to be the electrostatic energy of a uniformly charged layer grown during the elementary time step. Hence the growth probability of the presented non-equilibrium process obeys the equilibrium Gibbs-Boltzmann statistics. The results are related to the Onsager minimal dissipation principle and the minimum entropy production proposed by Prigogine for systems far from equilibria.