  A quantum model can be mapped to a classical model in one higher dimension.
Here we introduce a finite-temperature correlation measure based on a reduced
density matrix rho_A obtained by cutting the classical system along the
imaginary time (inverse temperature) axis. We show that the von-Neumann entropy
S_ent of rho_A shares many properties with the mutual information, yet is based
on a simpler geometry and is thus easier to calculate. For one-dimensional
quantum systems in the thermodynamic limit we proof that S_ent is non-extensive
for all temperatures T. For the integrable transverse Ising and XXZ models we
demonstrate that the entanglement spectra of rho_A in the limit T-> 0 are
described by free-fermion Hamiltonians and reduce to those of the regular
reduced density matrix---obtained by a spatial instead of an imaginary-time
cut---up to degeneracies.
