  The late-time evolution of the neutrino event rate from supernovae is
evaluated for Super-Kamiokande using simulated results of proto-neutron star
(PNS) cooling. In the present work we extend the result of Suwa et al. (2019)
[arXiv:1904.09996], which studied the dependence on the PNS mass, but focus on
the impact of the nuclear equation of state (EOS). We find that the neutrino
event rate depends on both the high-density and low-density EOS, where the
former determines the radius of the PNS and the latter affects its surface
temperature. Based on the present evaluation of the neutrino event rate we
propose a new analysis method to extract the time variability of the neutrino
average energy taking into account the statistical error in the observation.
