Quantifying Intrinsic Variability of Sagittarius A* Using Closure Phase Measurements of the Event Horizon Telescope

General relativistic magnetohydrodynamic (GRMHD) simulations of accretion disks and jets associated with supermassive black holes show variability on a wide range of timescales. On timescales comparable to or longer than the gravitational timescale $t_G=GM/c^3$, variation may be dominated by orbital dynamics of the inhomogeneous accretion flow. Turbulent evolution within the accretion disk is expected on timescales comparable to the orbital period, typically an order of magnitude larger than $t_G$. For Sgr A*, $t_G$ is much shorter than the typical duration of a VLBI experiment, enabling us to study this variability within a single observation. Closure phases, the sum of interferometric visibility phases on a triangle of baselines, are particularly useful for studying this variability. In addition to a changing source structure, variations in observed closure phase can also be due to interstellar scattering, thermal noise, and the changing geometry of projected baselines over time due to Earth rotation. We present a metric that is able to distinguish the latter two from intrinsic or scattering variability. This metric is validated using synthetic observations of GRMHD simulations of Sgr A*. When applied to existing multi-epoch EHT data of Sgr A*, this metric shows that the data are most consistent with source models containing intrinsic variability from source dynamics, interstellar scattering, or a combination of those. The effects of black hole inclination, orientation, spin, and morphology (disk or jet) on the expected closure phase variability are also discussed.