A circulating particle current and energy currents in a circular tube with a temperature difference

Network effects in a circulating particle current and energy currents are discussed in the system consisting of hard disks confined in a circular tube with a temperature difference. Here, two parts of the walls of the tube, as the thermal walls, are kept at different temperatures, so the system has two areas connecting these different thermal walls as a simple network. The temperatures of the thermal walls are imposed by stochastic boundary conditions for particles to contact with these walls. In this circular system, we show that the temperature difference induces, not only energy currents, but also a steady circulating particle current, in the tube. This particle current is regarded as a “thermal convection” in the sense that it flows from the high-temperature region to the low-temperature one in one connecting area while it flows in the opposite direction of the temperature difference in the other connecting area. We also discuss transport properties of the energy currents via these two connecting areas, such as their oscillatory behaviors as functions of the positions of the thermal walls or the width of the tube. Graphical abstract