It is conjectured that, in the asymptotic expansion of the Kashaev invariant of a
hyperbolic knot, the first coefficient is represented by the complex volume of the knot
complement, and the second coefficient is represented by a constant multiple of the
square root of the twisted Reidemeister torsion associated with the holonomy
representation of the hyperbolic structure of the knot complement. In particular, this
conjecture has been rigorously proved for some simple hyperbolic knots, for which the
second coefficient is presented by a modification of the square root of the
Hessian of the potential function of the hyperbolic structure of the knot
complement.
In this paper, we define an invariant of a parametrized knot diagram as a
modification of the Hessian of the potential function obtained from the parametrized
knot diagram. Further, we show that this invariant is equal (up to sign) to a
constant multiple of the twisted Reidemeister torsion for any two-bridge
knot.