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We consider a network of N noisy bistable elements with global time-delayedcouplings. In a two-state description, where elements are represented by Isingspins, the collective dynamics is described by an infinite hierarchy of coupledmaster equations which was solved at the mean-field level in the thermodynamiclimit. For a finite number of elements, an analytical description was deemed sofar intractable and numerical studies seemed to be necessary. In this paper weconsider the case of two interacting elements and show that a partialanalytical description of the stationary state is possible if the stochasticprocess is time-symmetric. This requires some relationship between thetransition rates to be satisfied.

Stochastic dynamics of N bistable elements with global time-delayed interactions: towards an exact solution of the master equations for finite N