  The reciprocity principle governs the symmetry in transmission of
electromagnetic and acoustic waves, as well as the diffusion of heat between
two points in space, with important consequences for thermal management and
energy harvesting. There has been significant recent interest in materials with
time-modulated properties, which have been shown to efficiently break
reciprocity for light, sound, and even charge diffusion. Quite surprisingly,
here we show that, from a practical point of view, time modulation cannot
generally be used to break reciprocity for thermal diffusion. We establish a
theoretical framework to accurately describe the behavior of diffusive
processes under time modulation, and prove that thermal reciprocity in dynamic
materials is generally preserved by the continuity equation, unless some
external bias or special material is considered. We then experimentally
demonstrate reciprocal heat transfer in a time-modulated device. Our findings
correct previous misconceptions regarding reciprocity breaking for thermal
diffusion, revealing the generality of symmetry constraints in heat transfer,
and clarifying its differences from other transport processes in what concerns
the principles of reciprocity and microscopic reversibility.
