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The notions of two-dimensional area, Killing fields and matter flux areintroduced in the setting of causal fermion systems. It is shown that forcritical points of the causal action, the area change of two-dimensionalsurfaces under a Killing flow in null directions is proportional to the matterflux through these surfaces. This relation generalizes an equation in classicalgeneral relativity due to Ted Jacobson to the setting of causal fermionsystems.

Two-Dimensional Area and Matter Flux in the Theory of Causal Fermion Systems