Ruo Cheng Huang of the Nanyang Technological University and colleagues from Beyond Institute for Theoretical Science (BITS) and Institute of Advanced Intelligence and Computing (IAIC) have defined time-ordered free energy (TOFE) as the maximum work obtainable from temporally correlated quantum systems, constrained by knowledge of only past events. The team developed a dynamic programming algorithm with linear time complexity relative to sequence length. This algorithm reveals that maximising energy gain at each step is not always optimal, with the key value identified as kBT ln 2. TOFE is a new metric quantifying the potential work obtainable from quantum systems evolving over time. The measurement accounts for an agent’s inability to foresee future states, limiting actions to responses based on past observations. The team demonstrated that consistently maximising energy gain at each step does not guarantee the highest overall energy harvest; instead, a different approach proves more effective. This measurement considers an agent’s limitations, acting only on past events, mirroring scenarios where future prediction is impossible. The team’s approach uses dynamic programming, solving complex problems by breaking them into simpler, overlapping subproblems. This finding challenges conventional approaches to sequential energy harvesting and opens questions about designing agents for temporally correlated quantum environments. Linear time complexity unlocks analysis of temporally correlated quantum systems A dynamic programming approach achieved linear scaling of time complexity with sequence length, a substantial improvement over previous exponential methods. This advancement enables the analysis of quantum state sequences previously considered intractable due to computational limitations, as sequences exceeding a few steps were beyond the reach of existing algorithms. Defining time-ordered free energy (TOFE) established a new benchmark for quantifying the maximum work obtainable from temporally correlated quantum systems operating under causal constraints. Work at Nanyang Technological University and A*STAR’s Centre for Quantum Technologies showed that enforcing temporal causality,