An exact density-functional closure for the two-dimensional discrete wormlike chain
Abstract
We formulate an exact density-functional description of the angularly discretized two-dimensional (2D) discrete wormlike chain (DWLC) under tension. The central result is a bond-local closure connecting the nearest-neighbor pair distribution Ci,i+1rs to the single-site angular densities ρir: Ci,i+1rsCi,i+100/(Ci,i+1r0Ci,i+10s)=eβ̅ rs, with the bond coupling β̅=βκε2/a. This relation follows directly from the connected Boltzmann weight of the quadratic bending interaction and permits exact integration of the entropy functional. Variational minimization then yields coupled self-consistent equations for the one- and two-site angular distributions, which we solve by fixed-point iteration. We establish the equivalence of this density-functional formulation to the exact transfer-matrix solution: the two approaches reproduce the angular marginals and force-extension curves to machine precision. The formulation also recovers the continuum 2D wormlike-chain behavior, including the rigid-rod and random-coil limits of the mean-square end-to-end distance. Using the segment length and persistence length taken directly from Mazur's short-DNA molecular-dynamics study, without additional fitting, the predicted bend-angle statistics agree with the simulation data within the estimated uncertainty. The closure structure extends naturally to nonharmonic local bending interactions and can also be interpreted inversely, allowing measured nearest-neighbor angular correlations to constrain effective coarse-grained bending potentials. These properties establish a direct connection between conformational statistics and local interactions and provide a density-level framework for treating interacting semiflexible-polymer systems.
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BibTeX
@misc{bakhti2026exact,
title = {{An exact density-functional closure for the two-dimensional discrete wormlike chain}},
author = {Benaoumeur Bakhti},
howpublished = {arXiv},
year = {2026},
month = aug,
doi = {10.48550/arxiv.2605.29743},
eprint = {2605.29743},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.29743},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - An exact density-functional closure for the two-dimensional discrete wormlike chain
AU - Benaoumeur Bakhti
PY - 2026
DA - 2026/08/31
PB - arXiv
DO - 10.48550/arxiv.2605.29743
UR - https://arxiv.org/abs/2605.29743
AB - We formulate an exact density-functional description of the angularly discretized two-dimensional (2D) discrete wormlike chain (DWLC) under tension. The central result is a bond-local closure connecting the nearest-neighbor pair distribution C_i,i+1^rs to the single-site angular densities ρ_i^r: C_i,i+1^rsC_i,i+1^00/(C_i,i+1^r0C_i,i+1^0s)=e^β̅ rs, with the bond coupling β̅=βκε^2/a. This relation follows directly from the connected Boltzmann weight of the quadratic bending interaction and permits exact integration of the entropy functional. Variational minimization then yields coupled self-consistent equations for the one- and two-site angular distributions, which we solve by fixed-point iteration. We establish the equivalence of this density-functional formulation to the exact transfer-matrix solution: the two approaches reproduce the angular marginals and force-extension curves to machine precision. The formulation also recovers the continuum 2D wormlike-chain behavior, including the rigid-rod and random-coil limits of the mean-square end-to-end distance. Using the segment length and persistence length taken directly from Mazur's short-DNA molecular-dynamics study, without additional fitting, the predicted bend-angle statistics agree with the simulation data within the estimated uncertainty. The closure structure extends naturally to nonharmonic local bending interactions and can also be interpreted inversely, allowing measured nearest-neighbor angular correlations to constrain effective coarse-grained bending potentials. These properties establish a direct connection between conformational statistics and local interactions and provide a density-level framework for treating interacting semiflexible-polymer systems.
ER -