I show how the holographic entropy bound can be derived from elementary flat-spacetime quantum field theory when the total energy of Fock states is constrained gravitationally. This energy constraint makes the Fock space dimension (whose logarithm is the maximum entropy) finite for both bosons and fermions. Despite the elementary nature of my analysis, it results in an upper limit on entropy in remarkable agreement with the holographic bound, and also provides a microscopic deviation of a more general entropy bound recently introduced by Gour.
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