The Nernst theorem and statistical entropy in a (1+1)-dimensional charged black hole

We derive the bosonic and fermionic entropies in (1 + 1)-dimensional charged black hole directly by using the quantum statistical method, The result is the same as the integral expression obtained by solving the wave equation approximately. Then we obtain the statistical entropy of the black hole by integration via the improved brick-wall method, membrane model. The derived entropy satisfies the thermodynamic relation. When the radiation temperature of the black hole tends to zero, so does the entropy. It obeys Nernst theorem. So it can be taken as Planck absolute entropy.