宏观系统的量子随机热力学：一种代数方法
Quantum stochastic thermodynamics of macroscopic systems: an algebraic approach
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中文总结 AI 辅助
该研究构建宏观量子系统热力学框架，基于少数可观测量测量统计进行粗粒度描述，推导粗粒度动力学第二定律及涨落定理，确定量子宏观功热概念，统一宏观与随机热力学，为分析量子动力学提供工具。
中文摘要 AI 辅助
我们构建了一个宏观量子系统热力学的框架。与需要完整密度矩阵的方法不同，该框架基于对少数可观测量的测量统计进行粗粒度描述。当可观测量对易时，结果定义经典宏观态，其熵由观测熵量化，考虑宏观态及其内微观态的不确定性。我们将此概念扩展到形成算子空间子代数的非对易可观测量，并利用杰恩斯原理定义介于冯·诺依曼熵和观测熵之间的依赖代数的熵。给定通过内部和/或环境诱导动力学连接的初始和最终测量集，我们推导了粗粒度动力学的第二定律。与基于冯·诺依曼熵的公式不同，我们的不等式捕捉了非酉环境诱导动力学和内部平衡的不可逆性。当系统最初处于内部平衡时，它具有通常的正熵产生形式，而修正项捕捉粗粒度忽略的非平衡资源。我们还推导了粗粒度热力学量的涨落定理。沿着测量方案的准静态路径，我们确定了满足第一和第二定律的量子宏观功和热的概念，包括通过外部约束或量子测量反作用操纵系统所受限的代数产生的额外功贡献。最后，我们将框架应用于示例，说明改变粗粒度方案的影响。我们的方法在真正的量子框架中统一了宏观和随机热力学，为分析复杂量子动力学奠定了通用、实验友好的工具箱基础。
英文摘要
We build a framework for the thermodynamics of macroscopic quantum systems. In contrast with approaches requiring access to the full density matrix, our framework relies on a coarse-grained description, based on measurement statistics of a few observables. When these observables commute, the outcomes define classical macrostates whose entropy is quantified by observational entropy, accounting for uncertainty about both the macrostate and the microstate within it. We extend this notion to non-commuting observables forming a subalgebra of the operator space, and use Jaynes' principle to define an algebra-dependent entropy interpolating between von Neumann and observational entropies. Given initial and final measurement sets, connected by internal and/or environment-induced dynamics, we derive a second law for the coarse-grained dynamics. Unlike formulations based on von Neumann entropy, our inequality captures irreversibility from both non-unitary environment-induced dynamics and internal equilibration. It takes the usual form of a positive entropy production when the system is initially at internal equilibrium, while correction terms capture nonequilibrium resources ignored by the coarse-graining. We also derive fluctuation theorems for coarse-grained thermodynamic quantities. Along a quasi-static path of measurement schemes, we identify quantum macroscopic notions of work and heat fulfilling the first and second laws, including an additional work contribution from manipulating the algebra to which the system is confined, through external constraints or quantum measurement backaction. Finally, we apply our framework to examples illustrating the impact of varying the coarse-graining scheme. Our approach unifies macroscopic and stochastic thermodynamics in a genuinely quantum framework, laying the basis for a versatile, experimentally friendly toolbox to analyze complex quantum dynamics.
