Equivalence Principle violation in metric-affine gravity and finite-temperature effects

Possible violations of the equivalence principle are investigated within the framework of metric-affine gravity and their connection to finite-temperature effects are highlighted. Thermal corrections to particle dynamics, originally derived in a quantum-field-theory setting, can be evaluated in a purely Riemannian framework and lead to a shift in the gravitational-to-inertial mass ratio. We show that the ensuing departure from universality of free fall can be also formulated in metric-affine gravity, where the presence of the non-metricity tensor modifies the Newtonian law in a way that closely parallels the finite-temperature scenario. Furthermore, we introduce a generalized Fermi-Walker derivative adapted to non-Riemannian contexts, which naturally reveals that no orthonormal tetrad can be propagated along an observer worldline. Although metric-affine gravity admits a pointwise realization of the Einstein equivalence principle in its gauge-theoretic, elementary-matter form, the new operator offers a direct geometric signature that this principle, in its modern formulation, is not retained in general. Potential tests of the analyzed effects are also discussed.