  It is commonly believed that the dissipative properties of superdense matter
play a negligible role in modeling gravitational waveforms from neutron star
inspirals. This study aims to investigate whether this presumption holds true
for the often neglected dissipative process associated with particle diffusion
in superconducting neutron stars. As we demonstrate, diffusion effects can
significantly impact the phase of the gravitational wave from the inspiral,
manifesting at a magnitude of a few tens of milliradians at large orbit
separations, equivalent to orbital frequencies of a few hertz. We also find
that dissipation resulting from particle diffusion might increase the neutron
star's temperature to approximately $10^7\rm K$ during the inspiral.
