Comment by hxtk

A Markov process is any process where if you have perfect information on the current state, you cannot gain more information about the next state by looking at any previous state.

Physics models of closed systems moving under classical mechanics are deterministic, continuous Markov processes. Random walks on a graph are non deterministic, discrete Markov processes.

You may further generalize that if a process has state X, and the prior N states contribute to predicting the next state, you can make a new process whose state is an N-vector of Xs, and the graph connecting those states reduces the evolution of the system to a random walk on a graph, and thus a Markov process.

Thus any system where the best possible model of its evolution requires you to examine at most finitely many consecutive states immediately preceding the current state is a Markov process.

For example, an LLM that will process a finite context window of tokens and then emit a weighted random token is most definitely a Markov process.