0 2000 4000 6000 8000 10000 Time (ps) -150 -100 -50 0 50 100 150 Velocity (m/s) $_{γ}$ = 0.50 pN ps $^{2}$/A2 $_{γ}$ = 1.48 pN ps $^{2}$/A2 FIG. S7: Time evolution of the velocity of the inner tube center of mass obtained from integration of Eq. (1) with the following parameters: F$_{vdw}$ = 1.92 nN, α = 8.08 pN nm/K, and a thermal gradient of 0.1 K/nm ( p ( t ) = 1). The inner and outer tube lengths were 5 nm and 1000 nm, respectively. 18