Correlation as a Source of Stochasticity in Continuum Models

Explore how molecular correlations introduce stochasticity in continuum models through this 38-minute conference talk by Keith Promislow from Michigan State University. Delve into the BBGKY hierarchy framework and understand how molecular dynamics models characterize material properties through pairwise interactions between N particles using partial differential equations for N-particle probability distribution functions. Learn about the mean-field limit where single particles couple to mean-fields generated by other particles, representing a significant reduction in complexity when joint probability distributions reduce to tensor products of single particle distributions. Examine the breakdown of this mean-field approach when small particle groups have successive interactions, such as water molecules in ion hydration shells, which generate correlations described by 2 and 3 particle joint distributions. Discover the impact of these correlations on hydrodynamic limits that enable further reduction to continuum systems, with particular focus on models involving particles with dipole moments like water molecules. Gain insights into the transition from deterministic to stochastic interaction modeling in electrochemistry through this comprehensive analysis of how microscopic correlations manifest as stochasticity at the continuum level.