Exploring the source of free energy is of practical use for thermodynamical systems. In the classical regime, the free energy change is independent of magnetism, as the Lorentz force is conservative. In contrast, here we find that the free energy change can be amplified by adding a magnetic field to driven quantum systems. Taking a recent experimental system as an example, the predicted amplification becomes 3-fold when adding a 10-tesla magnetic field under temperature 316 nanoKelvin. We further uncover the mechanism by examining the driving process. Through extending the path integral approach for quantum thermodynamics, we obtain a generalized free energy equality for both closed and open quantum systems. The equality reveals a decomposition on the source of the free energy change: one is the quantum work functional, and the other emerges from the magnetic flux passing through a closed loop of propagators. The result suggests a distinct quantum effect of magnetic flux and supports to extract additional free energy from the magnetic field.

探索自由能的来源在热力学系统中具有实际用途。在经典状态下，由于洛伦兹力是保守的，自由能的变化与磁场无关。相反，在这里我们发现可以通过向驱动的量子系统中添加磁场来放大自由能的变化。以最近的实验系统为例，当在316纳米开尔文温度下添加10特斯拉磁场时，预测的放大倍数变为3倍。我们通过检查驱动过程来进一步揭示该机制。通过扩展量子热力学的路径积分方法，我们获得了封闭和开放量子系统的广义自由能等式。平等揭示了自由能变化源的分解：一个是量子功函数，另一个来自穿过传播器闭环的磁通量。结果表明，磁通量具有明显的量子效应，并支持从磁场中提取更多的自由能。