Bi-Hamiltonian in Semiflexible Polymer as Strongly Coupled System

TL;DR

The paper addresses memory effects arising from cross-coupled, bi-Hamiltonian dynamics in semiflexible polymers, focusing on coarse-grained SWCNT models. It develops a diffusion-based description from the overdamped Smoluchowski equation within a Stochastic Thermodynamics framework, introducing a cross-term $\phi$ that couples $H_{\ell}$ and $H_{\theta}$. The key contributions include a finite-bath ensemble with a strongly coupled perturbation $\phi$ and validation via MD/CGMD SWCNT collision simulations, showing that heat-diffusion damping improves agreement with atomic-scale results. The work demonstrates that diffusion acts as a principled damping mechanism for memory effects in far-from-equilibrium nanoscale systems, enabling more accurate CGMD modeling of nonlinear dynamics and mode coupling. This approach provides a pathway to incorporate memory effects into CGMD of semiflexible polymers and potentially informs the design of nano-mechanical devices.

Abstract

The memory effect, which quantifies the interconnection between the target system and its environment, correlates states between distinct Hamiltonians. In this paper, we propose the diffusion process derived from Smoluchowski equation that can manifest the evolution of memory effect integration in non Markovian regime. The master equation from the Smoluchowski picture, within the framework of Stochastic Thermodynamics, justifies the use of the diffusion process. The numerical experiments using collision between semiflexible polymers like single walled carbon nanotubes(SWCNT) confirm the derivation and the justification of the usage of the heat diffusion to compensate the correlated momentum between two Hamiltonians that compose coarse grained system of SWCNT. The diffusion process governs the nonlinear motion in both equilibrium and far from equilibrium states.

Figures (4)

• Figure 1: A. a. Schematic figure of suspended SWCNT and a part of the structure that is equivalent to a CG particle in blue shade, b. Deformation variables for a part of the SWCNT shaded in Fig. A-a. $\Delta \ell$ and $\Delta \theta$ are the deformation along the tube length and angle. $\Delta r$ is the radial deformation, which is omitted. B. Evolution of the deformation along the bond length and angle direction at $t$ and $t+\Delta t$. The coordinate system used to measure deformation evolves with the macroscopic motion of the tube, therefore, the momentum defined along the coordinate system affected by Dzhanibekov effect.
• Figure 2: The initial configuration of the molecular dynamics(MD) simulation for the collision between two (5,5) SWCNTs (upper) and its CGMD model (below). Tube2 is artificially bent before the simulation and its trajectory is disregarded in the analysis. The data from Tube1, which receives the collision, is collected for normal mode decomposition and further analysis.
• Figure 3: The result of normal mode decomposition. The first mode along each Cartesian coordinate in the simple beads system was calculated for A. the MD simulation, B. CGMD simulation with Eq.(\ref{['eq:eq_go1']})$\sim$Eq.(\ref{['eq:eq_cro']}), and C. CGMD simulation without Eq.(\ref{['eq:eq_cro']}).
• Figure 4: The histogram of $\phi$ during A. in the MD simulation, B. the CGMD simulation with and without Eq.(\ref{['eq:eq_cro']}).