Time-ordered free energy in correlated quantum systems: An agentic approach

Abstract

How much work can an agent extract from a temporal sequence of quantum states when it can only operate online under causal constraints---deciding which energy extraction method to use with knowledge of what it has observed before? Here, we study this problem in the context of quantum state sequences that are potentially non-Markovian---generated by some underlying hidden Markov machine that the agent cannot observe. Using techniques from dynamic programming and computational mechanics, we present a method to identify the provably optimal agent strategy, with time complexity that scales linearly with sequence length. This motivates us to introduce the maximum work such agents can extract---time-ordered free energy(TOFE)---as a fundamental measure of free energy available in a temporally correlated quantum system subject to causal considerations.