Requisite ingredients for thermal rectification

The present work is devoted to an analytical investigation of the thermal rectification mechanism. More specifically, we attempt to find the requisite ingredients for such a phenomenon to occur. Starting from the linearization of the time evolution equations of anharmonic chains of oscillators, we propose some effective harmonic toy models with a potential that is dependent on temperature, and we investigate their steady heat currents. This unusual temperature-dependent potential is the footprint of nonlinearity in the final effective linear model. The approach is not restricted to any particular regime of heat transport. Our results show that thermal rectification holds in a system if it has asymmetric parameters related to its own structure, e.g., a graded particle mass distribution and some other parameters or features dependent on the inner temperatures that change as we invert the baths at the boundaries. The description of rectification in these simplified models, with minimal ingredients, shows that it is a ubiquitous phenomenon, and it may serve as a guide for further research.