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In the Jacobson formalism general relativity is obtained from thermodynamics.This is done by using the Bekenstein-Hawking entropy-area relation. However, asa black holes will gets smaller, its temperature will increase. This will causethe thermal fluctuations to also increase, and these will in turn correct theBekenstein-Hawking entropy-area relation. Furthermore, with the reduction inthe size of the black hole, quantum effects will also start to dominate. Justas the general relativity can be obtained from thermodynamics in the Jacobsonformalism, we propose that the quantum fluctuations to the geometry can beobtained from thermal fluctuations.

Quantum Fluctuations from Thermal Fluctuations in Jacobson Formalism