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Bit Threads: From Entanglement to Geometric Entropies

In this work, we attempt to construct bit thread configurations for various backgrounds using expressions from the covariant phase space formalism. We find that when the Ryu-Takayanagi surface is same as the horizon, such expressions are sufficient. In other cases, it differs by gradient of a harmonic function. We explore its relation to Wald and differential entropy, and re-express the first law of entanglement entropy in terms of bit threads. Inclusion of quantum effects imposes some constraints on the bulk entanglement via the dominant energy condition. We also apply our method to ascertain a bit thread configuration in a certain dynamical spacetime.