Heat-source transformation thermotics: from boundary-independent conduction to all-directional replication

All objects in nature are essentially heat sources due to their non-zero temperatures, but the control of them are seldom explored in the theory of transformation thermotics, which largely results from the complicated and uncontrollable parameters given by this theory. Here we put forward an equivalence operation to overcome this challenge, and then show analytical, simulation and experimental evidence for boundary-independent conduction and all-directional replication. The former represents the counterintuitive boundary-independent behavior of thermal conduction surrounded by arbitrary boundaries; the latter denotes a thermal copy of arbitrary shaped objects, which has the accurate shape of isotherms of the objects along all directions. The equivalence operation could be an applicable method for achieving uniform heating, boundary-independent cloaking, all-directional camouflaging, etc. Our results could also give hints for both freely controlling heat transfer and delicately designing similar conduction and replication in other disciplines like electrostatics and particle diffusion.