Thermodynamic transports in a circular system with a temperature difference

Thermodynamic transport phenomena in the system consisting of many hard-disks confined in a circular tube with a temperature difference are discussed. Here, temperatures on parts of the walls of the tube are imposed by stochastic boundary conditions for particles to contact with these thermal walls. In this system, the temperature difference induces, not only energy currents, but also a circulating particle current, inside the tube. Transport properties of these steady currents are discussed in various values of system parameters, such as the temperature difference, the particle density, the width of the tube, and the positions of the thermal walls.