量子系统的自主化与功算符的出现
Autonomization of Quantum Systems and the Emergence of the Work Operator
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中文总结 AI 辅助
研究量子尺度下功的估计难题，通过自主化受控能量转移确定功算符，推导量子涨落定理，纳入不完美控制并扩展到开放量子系统，解决了功是否为量子可观测量的争论。
中文摘要 AI 辅助
在量子尺度下功的估计仍是量子热力学的核心挑战。传统方法存在根本缺陷，其假设对量子系统的经典控制，却忽略了实现该控制的能量成本，这使功值的操作意义存疑。我们通过自主化受控能量转移来解决此问题，将驱动动力学嵌入更大量子系统的能量守恒演化中。功可明确等同于两系统间转移的能量，从而确定了驱动系统上的一个独特可观测量：功算符。我们通过推导量子涨落定理表明量子功算符规避了一个不可行定理，该定理在经典情形下恢复了雅津斯基等式。我们纳入了不完美控制并量化了对功统计的修正。将框架扩展到开放量子系统，我们得到了一个算符形式的第一定律，其中功、热和内能变化由约化系统上不同的算符表示。这些结果解决了关于功是否为量子可观测量的长期争论：一旦将控制系统包含在描述中而非视为外部的，功就是量子可观测量。
英文摘要
Estimation of work at the quantum scale remains a central challenge in quantum thermodynamics. Canonical approaches have a fundamental drawback: they assume classical control of the quantum system, as implicit in a time-dependent Hamiltonian. Yet the energetic cost of implementing this control is omitted and can exceed the system's energy scale by orders of magnitude, calling into question the operational significance of work values. We address this by autonomizing the controlled energy transfer, embedding the driven dynamics into an energy-conserving evolution on a larger quantum system. Work is then unambiguously identified with the energy transferred between the two systems, singling out a unique observable on the driven system: the work operator. We show that the quantum work operator evades a no-go theorem by deriving a quantum fluctuation theorem that recovers the Jarzynski equality in classical scenarios. We incorporate imperfect control and quantify corrections to work statistics. Extending the framework to open quantum systems, we obtain an operatorial first law in which work, heat, and internal-energy changes are represented by distinct operators on the reduced system. Together, these results settle the long-standing debate over whether work is a quantum observable: it is, once the controlling system is included in the description rather than treated as external.
