A model with two weakly coupled systems having opposite thermodynamic arrows of time is exhibited. The essential conceptual step is the phrasing of the problem as a two-time boundary value problem. Such a system could arise in a big bang-big crunch cosmology. Causal paradoxes, in the event of communication between the regions, are discussed and resolved. The main issue confronted in the present article is the nature and possibility of such communication. A degree of signaling may be possible, but is likely to be overwhelmed by noise.
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