Generalized Gravitational Entropy from Total Derivative Action

We investigate the generalized gravitational entropy from total derivative terms in the gravitational action. Following the method of Lewkowycz and Maldacena, we find that the generalized gravitational entropy from total derivatives vanishes. We compare our results with the work of Astaneh, Patrushev, and Solodukhin. We find that if total derivatives produced nonzero entropy, the holographic and the field-theoretic universal terms of entanglement entropy would not match. Furthermore, the second law of thermodynamics could be violated if the entropy of total derivatives did not vanish.Comment: 24 pages; v2: added references, Sec. 5.2 for corner entanglement, a toy model in Sec. 5.3, and minor corrections; v3: added one reference, published versio

FROST -- Fast row-stochastic optimization with uncoordinated step-sizes

In this paper, we discuss distributed optimization over directed graphs, where doubly-stochastic weights cannot be constructed. Most of the existing algorithms overcome this issue by applying push-sum consensus, which utilizes column-stochastic weights. The formulation of column-stochastic weights requires each agent to know (at least) its out-degree, which may be impractical in e.g., broadcast-based communication protocols. In contrast, we describe FROST (Fast Row-stochastic-Optimization with uncoordinated STep-sizes), an optimization algorithm applicable to directed graphs that does not require the knowledge of out-degrees; the implementation of which is straightforward as each agent locally assigns weights to the incoming information and locally chooses a suitable step-size. We show that FROST converges linearly to the optimal solution for smooth and strongly-convex functions given that the largest step-size is positive and sufficiently small.Comment: Submitted for journal publication, currently under revie