This isn't quite related to your question, but I think Markov chains made their debut in the original information theory paper by Shannon What? That paper even

This isn't quite related to your question, but I think Markov chains made their debut in the original information theory paper by Shannon What? That paper even says: Stochastic processes of the type described above are known mathematically as discrete Markoff processes and have been extensively studied in the literature; the corresponding footnote says "For a detailed treatment see M. Frechet ... 1938".