  We investigate the nonequilibrium back reaction on the Schwarzschild black
hole from the radiation field. The back reactions are characterized by the
membrane close to the black hole. When the membrane is thin, we found that
larger temperature difference can lead to more significant negative surface
tension, larger thermodynamic dissipation cost and back reaction in energy and
entropy as well as larger black hole area. This may be relevant to the
primordial black holes in early universe. Moreover, our nonequilibrium model
can resolve the inconsistency issue of the black hole back reaction under zero
mass limit in the equilibrium case. In the thick membrane case, the
nonequilibrium back reaction is found to be more significant than that in the
thin membrane case. The nonequilibrium temperature difference can increase the
energy and entropy loss as well as the thermodynamic dissipation of the black
hole and the membrane back reactions. The nonequilibrium dissipation cost
characterized by the entropy production rate appears to be significant compared
to the entropy rate radiated by the black hole under finite temperature
difference. This may shed light on the black hole information paradox due to
the information loss from the entropy production rate in the nonequilibirum
cases. The nonequilibrium thermodynamic fluctuations can also reflect the
effects of the back-reactions of the Hawking radiation on the evolution of a
black hole.

High Energy Physics - Theory