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In this paper we study the thermodynamics of black branes with a modulatedcomplex scalar in the context of bulk and boundary theories. The modulationinduces inhomogeneity to the dual field theory, anisotropic pressure, and branecharge to the bulk geometry. The first law of thermodynamics and the Smarrrelation are obtained using the off-shell ADT and the reduced actionformalisms. We discuss the prescription for the mass of black branes, whichrelies on relevant and marginal deformations in the dual field theory. One ofthe cases is the gravity dual to a ABJM model with a sinusoidal mass functiondepending on a spatial coordinate. This is the first study of the deformed ABJMmodel at finite temperature including bulk thermodynamics.

Thermodynamics of Inhomogeneously Mass-deformed ABJM Model and Pressure Anisotropy