Weak Coupling in Stochastic Systems

Weak coupling is defined as a coupling between components which affects only their `external statistics', `internal statistics' adapting to external statistics as they would if components were isolated. The energy and matter transfers that lead to the Gibbs distribution in statistical mechanics exemplify such a mechanism, as does the transfer of jobs in Jackson networks of processors. The class of components that show weak coupling under a certain class of communication rules is determined exactly, and generalizes the two examples mentioned.