  We study the thermal and chemical evolution during the Kelvin-Helmholtz phase
of the birth of a neutron star, employing neutrino opacities that are
consistently calculated with the underlying equation of state (EOS).
Expressions for the diffusion coefficients appropriate for general relativistic
neutrino transport in the equilibrium diffusion approximation are derived. The
diffusion coefficients are evaluated using a field-theoretical finite
temperature EOS that includes the possible presence of hyperons. The variation
of the diffusion coefficients is studied as a function of EOS and compositional
parameters. We present results from numerical simulations of protoneutron star
cooling for internal stellar properties as well as emitted neutrino energies
and luminosities. We discuss the influence of the initial stellar model, the
total mass, the underlying EOS, and the addition of hyperons on the evolution
of the protoneutron star and upon the expected signal in terrestrial detectors.
