Episodic memory and semantic memory produce very different subjective experiences yet rely on overlapping networks of brain regions for processing. Traditional approaches for characterizing functional brain networks emphasize static states of function and thus are blind to the dynamic information processing within and across brain regions. This study used information theoretic measures of entropy to quantify changes in the complexity of the brain's response as measured by magnetoencephalography while participants listened to audio recordings describing past personal episodic and general semantic events. Personal episodic recordings evoked richer subjective mnemonic experiences and more complex brain responses than general semantic recordings. Critically, we observed a trade-off between the relative contribution of local versus distributed entropy, such that personal episodic recordings produced relatively more local entropy whereas general semantic recordings produced relatively more distributed entropy. Changes in the relative contributions of local and distributed entropy to the total complexity of the system provides a potential mechanism that allows the same network of brain regions to represent cognitive information as either specific episodes or more general semantic knowledge.