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As in the case of Einstein or Lovelock gravity, the action of quarticquasitopological gravity has not a well-defined variational principle. In thispaper, we first introduce a surface term that makes the variation of quarticquasitopological gravity well defined. Second, we present the static chargedsolutions of quartic quasitopological gravity in the presence of a non linearelectromagnetic field. One of the branch of these solutions presents a blackbrane with one or two horizons or a naked singularity depending on the chargeand mass of the solution. The thermodynamic of these black branes areinvestigated through the use of the Gibbs free energy. In order to do this, wecalculate the finite action by use of the counterterm method inspired byAdS/CFT correspondence. Introducing a Smarr-type formula, we also show that theconserved and thermodynamics quantities of these solutions satisfy the firstlaw of thermodynamics. Finally, we present the charged rotating black branes in$(n+1)$ dimensions with $k\leq [n/2]$ rotation parameters and investigate theirthermodynamics.

Surface Terms of Quartic Quasitopological Gravity and Thermodynamics of Nonlinear Charged Rotating Black Branes