Recursive Work Extraction from Quantum Conditional Information

Abstract: Quantum superposition, a cornerstone of quantum mechanics, enables systems to exist in multiple states simultaneously, giving rise to probabilistic outcomes. In quantum information science, conditional entropy has become a key metric for quantifying uncertainty in one system given information about another, revealing non-classical correlations that transcend classical physics. This study examines the nature of quantum conditional entropy and reports two key findings. First, it demonstrates that probabilistic outcomes involving quantum superposition arise from work based on information about the eigenstate in a recursive process. Second, it proposes that this extractable work constitutes the energy available to living systems-a concept without a classical analogue-counteracting the natural tendency toward disorder.