Energy diffusion of simple networks under the spatiotemporal thermostats

We investigate the energy transport in simple networks consisting of one-dimensional nonlinear chain with self-coupled loop. The impacts of the loop length and coupling strength on the heat flux and spatiotemporal correlation functions of energy–momentum fluctuations are discussed via Langevin thermostats generated by spatiotemporal noise. For thermostats at different temperatures, the spatiotemporal ones can weaken the total heat flux of the system in comparison with the normal Langevin ones. The total heat flux will increase when the dispersal kernel or the loop length or the coupling strength increases, while the heat flux in the loop does not change as the dispersal kernel or the loop length increases, and decrease as the coupling strength increases. Then the underlying mechanism of heat flux can be well explained by the phonon spectra and Fourier’s law. For the thermostats at the same temperatures, it is shown that the peak of the propagating front for the trunk (PT) and the peak of the propagating front from the coupling position to the outer trunk (PC) do not change almost for the normal Langevin and spatiotemporal thermostats. The PT decreases and PC increases when the loop length or coupling strength increases. Our results may contribute to further understanding of thermal information appearing in coupled nanotubes, polymer chains and biological networks. Graphical abstract Heat flux J vs the coupling strength k. The red circle, blue triangle and green five-pointed star refer to the total heat flux, heat flux in the self-coupled loop and shortcut, respectively. The length of the FPU- $$\beta $$ β lattice $$N = 500,$$ N = 500 , coupling at $$i = 151, j =350$$ i = 151 , j = 350 .