  For classical lattice systems, the Dobrushin-Lanford-Ruelle theory of
boundary conditions states that the restriction of a global equilibrium state
to a subsystem can be obtained as an integral over equilibrium states of the
subsystem alone. The Hamiltonians for the subsystem are obtained by fixing a
configuration for the variables in the complement of the subsystem, or more
generally, by evaluating the full interaction Hamiltonian with respect to a
state for the complement. We provide examples showing that the quantum
mechanical version of this statement is false. It fails even if the subsystem
is classical, but embedded into a quantum environment. We suggest an
alternative characterization of the local restrictions of global equilibrium
states by inequalities involving only local data.
