A mathematical model is presented for the description of parallel Boltzmann machines. The framework is based on the theory of Markov chains and combines a number of previously known results into one generic model. It is argued that parallel Boltzmann machines maximize a function consisting of a weighted sum of the well-known consensus function and a pseudoconsensus function. The weighting is determined by the amount of parallelism used in the Boltzmann machine and turns out to be problem dependent.
Zwietering, P. J., & Aarts, E. H. L. (1991). Parallel Boltzmann machines : a mathematical model. Journal of Parallel and Distributed Computing, 13(1), 65-75. https://doi.org/10.1016/0743-7315(91)90110-U