A quantum mechanical model of Newtonian gravity as an entropic force

While many forces in nature are mediated by exchange of virtual field quanta, there are also effective forces which arise from complex systems driving thermodynamic free energies to their extrema. In particular, it has been conjectured that gravity could arise as such a thermal or entropic interaction, rather than through a fundamental quantum field. In this scenario, it is unclear how quantized matter would couple to gravity. Here, we study this issue by constructing a detailed, fully quantum-mechanical model which reproduces Newton's law of gravitation in the thermodynamic limit. The entropic model has thermal fluctuations which are observably different from ordinary perturbative quantum gravity, and we show how to experimentally distinguish the two models.