For simple setups, where the radiation field deviates not too far from thermodynamic equilibrium (< 10 %), corrections to the Planckian thermal emission spectrum can be calculated (and measured) from the statistical operator method, using the heat flux and the photon flux as additional constraints in the entropy maximazation procedure:
Now I am courious if similar considerations could be applied to the situation of an evaporating black hole. Can the information, orignally stored in an evaporating black hole, in principle be reconstracted from analyzing it`s nonequilibrium emission spectrum (obtained from including a sufficient larger number of additional relevant parameters as constraints in the statistical operator method)?
I`m pondering if one could describe an evaporating black hole applying nonequilibrium statistical mechanics such that the global mean temperature is not sufficient to describe its thermodynamic state and additional (microscopic) degrees of freedom (which are important to store the information of infalling objects too) must be taken into account. My question then is: Are these deviations from thermodynamic equilibrium translated to deviations of the spectrum of the Hawking radiation from Planck s law? And if so, can this in principle be used to reconstract the information stored in the microscopic degrees of freedom of the black hole?