量子轨迹上功与熵产生的联合统计
Joint statistics of work and entropy production along quantum trajectories
AI总结：
本文针对 Markovian 受驱量子系统，基于量子跳跃轨迹推导功与熵产生的联合统计公式，给出联合细致涨落定理及含量子涨落项的修正 FDR。
摘要：
在热力学中，当系统被驱动到远离平衡态时，熵产生和功分别量化不可逆性与有用能量的消耗。对于量子系统，这些量可以在随机层面上通过以量子跳跃轨迹展开系统演化来识别。我们在此推导了一个通用公式，用于计算 Markovian 受驱量子系统中功与熵产生的联合统计，该系统的瞬时稳态具有 Gibbs 形式。如果受驱系统始终保持接近瞬时 Gibbs 态，我们证明，只要满足细致平衡，相应的双变量累积量生成函数就蕴含一个联合细致涨落定理。作为推论，我们推导了一个仅针对熵产生的修正涨落–耗散关系（FDR），适用于任意稳态之间的跃迁以及违反细致平衡的系统。该 FDR 包含一项源于真正量子涨落的项，并将经典热力学中的类似关系扩展到量子区域。
英文摘要：
In thermodynamics, entropy production and work quantify irreversibility and the consumption of useful energy, respectively, when a system is driven out of equilibrium. For quantum systems, these quantities can be identified at the stochastic level by unravelling the system's evolution in terms of quantum jump trajectories. We here derive a general formula for computing the joint statistics of work and entropy production in Markovian driven quantum systems, whose instantaneous steady-states are of Gibbs form. If the driven system remains close to the instantaneous Gibbs state at all times, we show that the corresponding two-variable cumulant generating function implies a joint detailed fluctuation theorem so long as detailed balance is satisfied. As a corollary, we derive a modified fluctuation-dissipation relation (FDR) for the entropy production alone, applicable to transitions between arbitrary steady-states, and for systems that violate detailed balance. This FDR contains a term arising from genuinely quantum fluctuations, and extends an analogous relation from classical thermodynamics to the quantum regime.
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