Bi-Hamiltonian in Semiflexible Polymer as Strongly Coupled System

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.