  Phase modulation has scarcely been mentioned in diffusive systems since the
diffusion process does not carry momentum like waves. Recently, the
non-Hermitian physics provides a new perspective for understanding diffusion
and shows prospects in the phase regulation of heat flow, for example, the
discovery of anti-parity-time (APT) symmetry in diffusive systems. The precise
control of thermal phase however remains elusive hitherto and can hardly be
realized in APT-symmetric thermal systems due to the existence of phase
oscillation. Here we construct the counterpart of APT-symmetric diffusive
systems, i.e., PT-symmetric diffusive systems, which can achieve complete
suppression of thermal phase oscillation. We find the real coupling of
diffusive fields can be readily established through a strong convective
background, where the decay-rate detuning is enabled by thermal metamaterial
design. Moreover, we observe phase transition of PT symmetry breaking in
diffusive systems with the symmetry-determined amplitude distribution and phase
regulation of coupled temperature fields. Our work uncovers the existence of
PT-symmetry in dissipative energy exchanges and provides a unique approach for
harnessing the mass transfer of particles, the wave propagation in strongly
scattering systems as well as thermal conduction.
