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In this paper we discuss the thermodynamics of the apparent horizon in $F(R)$Ho\v{r}ava-Lifshitz gravity in equilibrium and non-equilibrium ensembles. Weshow that the second law of thermodynamics can be satisfied in this nonrelativistic theory.

First and Second Laws of Thermodynamics in Modified Ho\v{r}ava-Lifshitz $F(R)$ Gravity