  Using the conformal equivalence of translational KMS states on chiral
theories with dilational KMS states obtained from restricting the vacuum state
to an interval (the chiral inversion of the Unruh-effect) it was shown in a
previous publications that the diverging volume (length) factor of the
thermodynamic limit corresponds to the logarithmic increase in the attenuation
length of the localization-caused vacuum polarization cloud near the causal
boundary. This is not a coincidence but rather a structural consequence of the
fact that both operator algebras are of the same unique von Neumann type which
is completely different from that met in quantum mechanical algebras. Together
with the technique of holographic projection this leads to the universal area
proportionality. The main aim in this paper is to present a derivation which is
more in the spirit of recent work on entanglement entropy in condensed matter
physics, especially to that of the replica trick as used by Cardy and
collaborators. The essential new ingredient is the use of the split property
which already has shown its constructive power in securing the existence of
models of factorizing theories.
