Emergent Gravity from Quantum Information Flow: A Modified Dirac Perspective

We present a unified thermodynamic framework in which the flow of quantum information — described covariantly by the entropy current vector s^μ-- couples to fermionic matter and simultaneously provides the microphysical origin of spacetime geometry. The Dirac equation is modified as (iℏγ^μ ∂_μ-mc+λγ^μ s_μ)ψ=0, where dimensional analysis identifies λ as a coupling constant of mass dimension [λ]=-2, naturally placing the theory as a low-energy effective field theory. The modified dispersion relation E=-λs^0 c±c√(p^2+m^2 c^2 ) shows that uniform entropy flow produces only an overall energy shift, while non-uniform flows induce a complete gauge-like structure in the non-relativistic limit: the spatial entropy current s acts as a vector potential, and its curl generates an effective magnetic field B_eff=(λ/m)∇×s, driving spin precession via ω_entropy=(λ/m)∇×s. Extending the Proca-type dynamics of s^μ to curved spacetime with non-minimal curvature coupling, we quantize the entropy flow field and integrate out its quantum fluctuations. In this framework, the Einstein-Hilbert action emerges as the low-energy effective action, with Newton's constant Gdetermined by the entropy field's vacuum expectation value. The linearized theory yields a massive spin-2 excitation -- the emergent graviton -- with dispersion E^2=p^2+m_s^2, where the entropy field mass m_s is constrained by LIGO/Virgo gravitational-wave observations to m_s≲10^(-20)eV. Using STAR data on Λ hyperon global spin polarization in heavy-ion collisions, we estimate λ∼10^(-7)-10^(-5) GeV^(-2), corresponding to an entropy-flow energy scale Λ_λ∼10^2-10^3GeV. This framework naturally connects to Jacobson's thermodynamic gravity, Verlinde's entropic gravity, and the generalized second law ∇_μ s^μ≥0, providing a quantum-information theoretic foundation for the emergence of spacetime and a concrete, testable realization of gravity as an entropic phenomenon.