A Nonequilibrium Statistical-mechanics Approach to Onsager-Joyce-Montegory Theory
Time: 2021-10-15
Published By: He Liu
Speaker(s): Chenyang Chen (PKU)
Time: 15:15-17:00 October 21, 2021
Venue: Room 77201, Jingchunyuan 78, BICMR
We are interested in characterizing large time coherent structures of a 2-D stochastic vortex dynamic on torus involving three limits taken one at a time. First, the uniqueness for an associated first order Hamilton-Jacobi equation in space of probability measures is established and with this result we prove a large deviation principle in probability-measure-valued path spaces when number of vortices go to infinity. Action functional for the large deviation problem can be expressed using a special control partial differential equation. Then we prove the large time limit of the rate function is exactly the entropy functional of probability distributions, which is independent of the inviscid limit. Hence in the sense of statistical mechanics, we derive an equilibrium micro-canonical variational principle, originally proposed by Onsager, from a non-equilibrium stochastic model by first principle.
