### Abstract

The stable conformations and dynamical fluctuations of polymers and macromolecules are governed by the underlying single-molecule free energy surface. By integrating ideas from dynamical systems theory with nonlinear manifold learning, we have recovered single-molecule free energy surfaces from univariate time series in a single coarse-grained system observable. Using Takens' Delay Embedding Theorem, we expand the univariate time series into a high dimensional space in which the dynamics are equivalent to those of the molecular motions in real space. We then apply the diffusion map nonlinear manifold learning algorithm to extract a low-dimensional representation of the free energy surface that is diffeomorphic to that computed from a complete knowledge of all system degrees of freedom. We validate our approach in molecular dynamics simulations of a C24H50 n-alkane chain to demonstrate that the two-dimensional free energy surface extracted from the atomistic simulation trajectory is - subject to spatial and temporal symmetries - geometrically and topologically equivalent to that recovered from a knowledge of only the head-to-tail distance of the chain. Our approach lays the foundations to extract empirical single-molecule free energy surfaces directly from experimental measurements.

Original language | English (US) |
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Article number | 032412 |

Journal | Physical Review E |

Volume | 93 |

Issue number | 3 |

DOIs | |

State | Published - Mar 21 2016 |

### ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Statistics and Probability
- Condensed Matter Physics

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## Cite this

*Physical Review E*,

*93*(3), [032412]. https://doi.org/10.1103/PhysRevE.93.032412