Quantum Fluctuations from Thermal Fluctuations in Jacobson Formalism

n the Jacobson formalism general relativity is obtained from thermodynamics. 
This is done by using the Bekenstein-Hawking entropy-area relation.
However, as a black holes will gets smaller, its temperature will increase. 
This will cause the thermal fluctuations to also increase,
and these will in turn correct the Bekenstein-Hawking entropy-area relation. 
Furthermore, with the reduction in the size of the black hole, quantum
effects will also start to dominate. Just as the  general relativity can be 

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