We derive novel results on the ergodic theory of irreducible, aperiodicMarkov chains . We show how to optimally steer the network flow to a stationary distribution over a finite or infinite time horizon . Optimality is with respectto an entropic distance between distributions on feasible paths . A notion of temperature is defined for Boltzmann distributions on networks, and problems analogous to cooling (in thiscase, for evolutions in discrete space and time) are discussed .

Author(s) : Yongxin Chen, Tryphon T. Georgiou, Michele Pavon

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Keywords : distributions - time - networks - - paths -

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