  Second sound and heat diffusion in single-walled carbon nanotubes (SWCNT) is
well-known phenomena which is related to the high thermal conductivity of this
material. In this paper, we have shown that the heat diffusion along the tube
axis affects the macroscopic motion of SWCNT and adapting this phenomena to
coarse-grained model can improve the precision of the coarse-grained molecular
dynamics (CGMD) exceptionally. The nonlinear macroscopic motion of SWCNT in the
free thermal vibration condition in adiabatic environment is demonstrated in
the most simplified version of CG modeling as maintaining finite temperature
and total energy with suggested dissipation process derived from internal heat
diffusion. The internal heat diffusion related to the cross correlated momentum
from different potential energy functions is considered, and it can reproduce
the nonlinear dynamic nature of SWCNTs without external thermostatting in CG
model. Memory effect and thermostat with random noise distribution are not
included, and the effect of heat diffusion on memory effect is reviewed through
Mori-Zwanzig formalism. This diffusion shows perfect syncronization of the
motion between that of CGMD and MD simulation, which is started with initial
conditions from the molecular dynamics (MD) simulation. The heat diffusion
related to this process has shown the same dispersive characteristics to second
wave in SWCNT. This replication with good precision indicates that the internal
heat diffusion process is the essential cause of the nonlinearity of the tube.
The nonlinear dynamic characteristics from the various scale of simple beads
systems are examined with expanding its time step and node length
simultaneously.
