量子轨迹中表观第二定律违反的边界
Bounds for Apparent Second-Law Violations in Quantum Trajectories
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中文总结 AI 辅助
该研究针对量子轨迹中表观第二定律违反问题，通过引入动力学不对称项构建相关统计量，推导得到经平局修正的符号统计量下界，并在两类模型中验证了定理的有效性。
中文摘要 AI 辅助
负随机熵产生通常被称为表观第二定律违反。然而，在一般量子轨迹动力学中，物理熵产生σ无需满足正向详细涨落定理。一种通用的任意耦合形式确定了动力学不对称项σ*，将其补充为Ω=σ+σ*，其平均值为⟨Ω⟩=Σ+Σ*。我们证明，在反转奇轨迹可观测量中，似然比符号是最优的，并利用这一事实将已确立的尖锐涨落定理下界转移到经平局修正的物理符号统计量Π_σ=Pr(σ<0)+Pr(σ=0)/2。当Pr(σ=0)=0时，结果为Pr(σ<0)≥[1−⟨Ω⟩/g(⟨Ω⟩)]/2，其中g是映射a→a tanh(a/2)的逆函数。物理积分涨落定理同时抑制大的负事件，产生定量的“频繁但温和”定律，而符号不平衡则对隐藏平均值Σ*进行下界约束。我们明确构建了测量记录协议，并在随机有限耦合碰撞模型以及与热辅助系统相互作用的相干驱动量子比特中对经平局修正的定理进行了说明和数值验证。
英文摘要
Negative stochastic entropy production is commonly called an apparent violation of the second law. In general quantum-trajectory dynamics, however, the physical entropy production $σ$ need not obey a forward detailed fluctuation theorem. A general arbitrary-coupling formulation identifies a dynamical-asymmetry term $σ^\ast$ that completes it into $Ω=σ+σ^\ast$, whose mean is $\langleΩ\rangle=Σ+Σ^\ast$. We prove that the likelihood-ratio sign is optimal among reversal-odd trajectory observables and use this fact to transfer an established sharp fluctuation-theorem floor to the tie-corrected physical sign statistic $Π_σ=\Pr(σ<0)+\Pr(σ=0)/2$. When $\Pr(σ=0)=0$, the result reads $\Pr(σ<0)\ge[1-\langleΩ\rangle/g(\langleΩ\rangle)]/2$, where $g$ is the inverse of $a\mapsto a\tanh(a/2)$. The physical integral fluctuation theorem simultaneously suppresses large negative events, producing a quantitative ``frequent but mild'' law, while the sign imbalance lower-bounds the hidden mean $Σ^\ast$. We formulate the measured-record protocol explicitly and illustrate and numerically audit the tie-corrected theorem in random finite-coupling collision models and a coherently driven qubit interacting with thermal ancillas.
