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We use an unconventional diagrammatic approach to formulate $CPT$ andunitarity constraints for higher-order $CP$ asymmetries entering the sourceterm in the Boltzmann equation. Usually, the reaction rate asymmetries in theseconstraints are computed within the classical kinetic theory, usingzero-temperature quantum field theory to describe particles' interactions. Weapproximate the rates, otherwise obtained within the closed-time-pathformalism, in terms of diagrams drawn on a cylindrical surface and theirholomorphic cuts. The resulting equilibrium asymmetry constraints incorporatethermal-mass effects and allow tracking the cancellations of reaction rateasymmetries computed with quantum statistics. We use the top Yukawa correctionsto the asymmetries in the seesaw type-I leptogenesis as an example.

$CPT$ and unitarity constraints for higher-order $CP$ asymmetries at finite temperature