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Inspired from the inflation brane world cosmology, we study thethermodynamics of a black hole solution in two dimensional dilaton gravity withan arctangent potential background. We first derive the two dimensional blackhole geometry, then we examine its asymptotic behaviors. More precisely, wefind that such behaviors exhibit properties appearing in some known casesincluding the Anti de Sitter and the Schwarzchild black holes. Using thecomplex path method, we compute the Hawking radiation. The entropy function canbe related to the value of the potential at the horizon.

On Thermodynamics of 2d Black Holes in Brane Inflationary Potentials