The Lund Area Law describes the probability for the production of a
set of colourless hadrons from an initial set of partons, in the Lund
string fragmentation model. It was derived from classical probability
concepts but has later been interpreted as the result of gauge
invariance in terms of the Wilson gauge loop integrals. In this paper
we will present a general method to implement the Area Law for a
multi-gluon string state. In this case the world surface of the
massless relativistic string is a geometrically bent (1+1)-dimensional
surface embedded in the (1+3)-dimensional Minkowski space. The
partonic states are in general given by a perturbative QCD cascade and
are consequently defined only down to a cutoff in the energy momentum
fluctuations. We will show that our method defines the states down to
the hadronic mass scale inside an analytically calculable scenario.
We will then show that there is a differential version of our process
which is closely related to the generalised rapidity range \lambda,
which has been used as a measure on the partonic states. We identify
\lambda as the area spanned between the directrix curve (the curve
given by the parton energy momentum vectors laid out in colour order,
which determines the string surface) and the average curve (to be
called the P-curve) of the stochastic X-curves (curves obtained when
the hadronic energy-momentum vectors are laid out in rank order).
Finally we show that from the X-curve corresponding to a particular
stochastic fragmentation situation it is possible to reproduce the
directrix curve (up to one starting vector and a set of sign choices,
one for each hadron). This relationship provides an analytical
formulation of the notion of Parton-Hadron Duality. The whole effort
is made in order to get a new handle to treat the transition region
between where we expect perturbative QCD to work and where the
hadronic features become noticeable.