On Reversible Markov Chains and Maximization of Directed Information
In this paper, the authors consider a dynamical system, whose state is an input to a memory-less channel. The state of the dynamical system is affected by its past, an exogenous input, and causal feedback from the channel's output. They consider maximizing the directed information between the input signal and the channel output, over all exogenous input distributions and/or dynamical system policies. They demonstrate that under certain conditions, reversibility of a Markov chain implies directed information is maximized.