Fig. 1: Transport processes in dynamic materials under time modulation.
From: Reciprocity of thermal diffusion in time-modulated systems
a Non-reciprocal propagation of electromagnetic wave can be induced by spatial-temporally modulating the electric permittivity ε(x,t) as a traveling wave (with speed v0). b Non-reciprocal diffusion of electric charges can be induced by spatial-temporally modulating the capacitance Ce(x,t) and electric conductivity σ(x,t). c The reciprocity of heat transfer cannot be broken by modulating the density ρ(x,t) and thermal conductivity κ(x,t) since it is preserved by the continuity equation. Following the law, mass movements v(x,t) (green arrows) must exist to achieve density modulation. d, e Two types of mass movements (dark gray spheres): d along the heat transfer path (gray region). e moving in and out of the heat transfer path.
