Entropy of Extremal Black Holes in Two Dimensions

In this paper we apply the entropy function formalism to the two-dimensional black hole which come from the compactification of the heterotic string theory with the dilaton coupling function. We find the Bekenstein-Hawking entropy from the value of the entropy function at its saddle point. Also we consider higher derivative terms. After that we apply the entropy function formalism to the Jackiw-Teitelboim (JT) model where we consider the effect of string-loop to this model. (authors)