Energetic advantages for quantum agents in online execution of complex strategies

Agents often execute complex strategies -- adapting their response to each input stimulus depending on past observations and actions. Here, we derive the minimal energetic cost for classical agents to execute a given strategy, highlighting that they must dissipate a certain amount of heat with each decision beyond Landauer's limit. We then prove that quantum agents can reduce this dissipation below classical limits. We establish the necessary and sufficient conditions for a strategy to guarantee quantum agents have energetic advantage, and illustrate settings where this advantage grows without bound. Our results establish a fundamental energetic advantage for agents utilizing quantum processing to enact complex adaptive behaviour.