Agentic Information Theory: Ergodicity and Intrinsic Semantics of Information Processes

We develop information theory for the temporal behavior of memoryful agents moving through complex -- structured, stochastic -- environments. We introduce information processes -- stochastic processes produced by cognitive agents in real-time as they interact with and interpret incoming stimuli. We provide basic results on the ergodicity and semantics of the resulting time series of Shannon information measures that monitor an agent's adapting view of uncertainty and structural correlation in its environment.