title: Shared information in stationary states of stochastic processes.
abstract: We present four estimators of the shared information (or interdepency) in ground states given that the coefficients appearing in the wave function are all real non-negative numbers and therefore can be interpreted as probabilities of configurations. Such ground states of Hermitian and non-Hermitian Hamiltonians can be given, for example, by superpositions of valence bond states which can describe equilibrium but also stationary states of stochastic models. We consider in detail the last case, the system being a classical not a quantum one. Using analytical and numerical methods we compare the values of the estimators in the directed polymer and the raise and peel models which have massive, conformal invariant and nonconformal invariant massless phases. We show that like in the case of the quantum problem, the estimators verify the area law with logarithmic corrections when phase transitions take place.
authors.affiliation: Instituto de Física de São Carlos, Universidade de São Paulo, Caixa Postal 369, 13560-590 São Carlos, SP, Brazil.
authors.forename: F C
authors.initials: FC
authors.lastname: Alcaraz
authors.forename: V
authors.initials: V
authors.lastname: Rittenberg
authors.forename: G
authors.initials: G
authors.lastname: Sierra