  We investigate the relations between black hole thermodynamics and
holographic transport coefficients in this paper. The formulae for DC
conductivity and diffusion coefficient are verified for electrically
single-charged black holes. We examine the correctness of the proposed
expressions by taking charged dilatonic and single-charged STU black holes as
two concrete examples, and compute the flows of conductivity and diffusion
coefficient by solving the linear order perturbation equations. We then check
the consistence by evaluating the Brown-York tensor at a finite radial
position. Finally, we find that the retarded Green functions for the shear
modes can be expressed easily in terms of black hole thermodynamic quantities
and transport coefficients.
