Non-Equilibrium Steady State Simulator

A chain of thermally coupled cells sits between a hot reservoir and a cold one. Energy diffuses cell-to-cell at a tunable rate, and the two end cells are held fixed at the reservoir temperatures. As long as those reservoirs differ, the chain settles into a non-equilibrium steady state: a fixed temperature profile carrying a constant, nonzero heat flux and producing entropy at a constant positive rate — the system keeps exchanging energy forever without ever reaching zero flow. Push the temperature difference to zero and the same lattice relaxes into ordinary thermodynamic equilibrium, where flux and entropy production both vanish, showing that equilibrium is simply the zero-gradient special case of the same steady-state physics.