### Abstract

A family of collective variables is proposed to perform exact dynamical coarse-graining even in systems without time scale separation. More precisely, it is shown that these variables are not slow in general, yet satisfy an overdamped Langevin equation that statistically preserves the sequence in which any regions in collective variable space are visited and permits to calculate exactly the mean first passage times from any such region to another. The role of the free energy and diffusion coefficient in this overdamped Langevin equation is discussed, along with the way they transform under any change of variable in collective variable space. These results apply both to systems with and without inertia, and they can be generalized to using several collective variables simultaneously. The view they offer on what makes collective variables and reaction coordinates optimal breaks from the standard notion that good collective variable must be slow variable, and it suggests new ways to interpret data from molecular dynamics simulations and experiments.

Original language | English (US) |
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Article number | 044109 |

Journal | Journal of Chemical Physics |

Volume | 141 |

Issue number | 4 |

DOIs | |

State | Published - Jul 28 2014 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

*Journal of Chemical Physics*,

*141*(4), [044109]. https://doi.org/10.1063/1.4890367

**Exact dynamical coarse-graining without time-scale separation.** / Lu, Jianfeng; Vanden Eijnden, Eric.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 141, no. 4, 044109. https://doi.org/10.1063/1.4890367

}

TY - JOUR

T1 - Exact dynamical coarse-graining without time-scale separation

AU - Lu, Jianfeng

AU - Vanden Eijnden, Eric

PY - 2014/7/28

Y1 - 2014/7/28

N2 - A family of collective variables is proposed to perform exact dynamical coarse-graining even in systems without time scale separation. More precisely, it is shown that these variables are not slow in general, yet satisfy an overdamped Langevin equation that statistically preserves the sequence in which any regions in collective variable space are visited and permits to calculate exactly the mean first passage times from any such region to another. The role of the free energy and diffusion coefficient in this overdamped Langevin equation is discussed, along with the way they transform under any change of variable in collective variable space. These results apply both to systems with and without inertia, and they can be generalized to using several collective variables simultaneously. The view they offer on what makes collective variables and reaction coordinates optimal breaks from the standard notion that good collective variable must be slow variable, and it suggests new ways to interpret data from molecular dynamics simulations and experiments.

AB - A family of collective variables is proposed to perform exact dynamical coarse-graining even in systems without time scale separation. More precisely, it is shown that these variables are not slow in general, yet satisfy an overdamped Langevin equation that statistically preserves the sequence in which any regions in collective variable space are visited and permits to calculate exactly the mean first passage times from any such region to another. The role of the free energy and diffusion coefficient in this overdamped Langevin equation is discussed, along with the way they transform under any change of variable in collective variable space. These results apply both to systems with and without inertia, and they can be generalized to using several collective variables simultaneously. The view they offer on what makes collective variables and reaction coordinates optimal breaks from the standard notion that good collective variable must be slow variable, and it suggests new ways to interpret data from molecular dynamics simulations and experiments.

UR - http://www.scopus.com/inward/record.url?scp=84905656925&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84905656925&partnerID=8YFLogxK

U2 - 10.1063/1.4890367

DO - 10.1063/1.4890367

M3 - Article

VL - 141

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 4

M1 - 044109

ER -