Age-related declines in memory may be due in part to changes in the complexity of neural activity in the aging brain. Electrophysiological entropy provides an accessible measure of the complexity of ongoing neural activity. In the current study, we calculated the permutation entropy of the electroencephalogram (EEG) during encoding of relevant (to be learned) and irrelevant (to be ignored) stimuli by younger adults, older adults, and older cognitively declined adults. EEG entropy was differentially sensitive to task requirements across groups, with younger and older controls exhibiting greater control of encoding-related activity than older declined participants. Task sensitivity of frontal EEG during encoding predicted later retrieval, in line with previous evidence that cognitive decline is associated with reduced ability to self-initiate encoding-related processes.