Petrov-Galerkin methods for the construction of non-Markovian dynamics preserving nonlocal statistics

Huan Lei, Xiantao Li

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


A common observation in coarse-graining a molecular system is the non-Markovian behavior, primarily due to the lack of scale separations. This is reflected in the strong memory effect and the non-white noise spectrum, which must be incorporated into a coarse-grained description to correctly predict dynamic properties. To construct a stochastic model that gives rise to the correct non-Markovian dynamics, we propose a Galerkin projection approach, which transforms the exhausting effort of finding an appropriate model to choosing appropriate subspaces in terms of the derivatives of the coarse-grained variables and, at the same time, provides an accurate approximation to the generalized Langevin equation. We introduce the notion of fractional statistics that embodies nonlocal properties. More importantly, we show how to pick subspaces in the Galerkin projection so that those statistics are automatically matched.

Original languageEnglish (US)
Article number184108
JournalJournal of Chemical Physics
Issue number18
StatePublished - May 14 2021

All Science Journal Classification (ASJC) codes

  • General Physics and Astronomy
  • Physical and Theoretical Chemistry


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