  For "static memory materials" the bulk properties depend on boundary
conditions. Such materials can be realized by classical statistical systems
which admit no unique equilibrium state. We describe the propagation of
information from the boundary to the bulk by classical wave functions. The
dependence of wave functions on the location of hypersurfaces in the bulk is
governed by a linear evolution equation that can be viewed as a generalized
Schr\"odinger equation. Classical wave functions obey the superposition
principle, with local probabilities realized as bilinears of wave functions.
For static memory materials the evolution within a subsector is unitary, as
characteristic for the time evolution in quantum mechanics. The
space-dependence in static memory materials can be used as an analogue
representation of the time evolution in quantum mechanics - such materials are
"quantum simulators". For example, an asymmetric Ising model on a Euclidean
two-dimensional lattice represents the time evolution of free relativistic
fermions in two-dimensional Minkowski space.
