In this paper, we explore the properties of proto-neutron star matter. The relativistic finite-temperature Green function formalism is used to derive the equations which determine the properties of such matter. The calculations are performed for the relativistic non-linear mean-filed theory, where different combinations of lepton number and entropy have been investigated. All particles of the baryon octet as well as all electrically charged states of the Δ isobar have been included in the calculations. The presence of all these particles is shown to be extremely temperature (entropy) dependent, which should have important consequences for the evolution of proto-neutron stars to neutron stars as well as the behavior of neutron stars in compact star mergers.

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