标题： 一种统一的单位残差度量框架，用于量化耗散 显示英文标题

标题： A unified framework of unitarily residual measures for quantifying dissipation

摘要： 开放量子系统由单位和非单位动力学共同支配，耗散来自后者。 传统的量子散度度量，如量子相对熵，在单位连接的状态之间即使散度为正也无法考虑非单位导向的耗散。 我们引入了一个框架，通过隔离量子动力学的非单位部分来量化耗散。 我们通过单位变换在厄米特算子之间定义等价关系，并表征所得的商集。 通过建立这个商集与有序分量实向量集之间的同构关系，我们诱导出在单位演化下不变的散度度量，我们称之为单位残余度量。 这些单位残余度量继承了如单调性和凸性等性质，并在某些情况下对应于排序本征值分布之间的经典信息散度。 我们的结果为量化开放量子系统的耗散提供了一个强有力的工具，推动了量子热力学的理解。 显示英文摘要

摘要： Open quantum systems are governed by both unitary and non-unitary dynamics, with dissipation arising from the latter. Traditional quantum divergence measures, such as quantum relative entropy, fail to account for the non-unitary oriented dissipation as the divergence is positive even between unitarily connected states. We introduce a framework for quantifying the dissipation by isolating the non-unitary components of quantum dynamics. We define equivalence relations among hermitian operators through unitary transformations and characterize the resulting quotient set. By establishing an isomorphism between this quotient set and a set of real vectors with ordered components, we induce divergence measures that are invariant under unitary evolution, which we refer to as the unitarily residual measures. These unitarily residual measures inherit properties such as monotonicity and convexity and, in certain cases, correspond to classical information divergences between sorted eigenvalue distributions. Our results provide a powerful tool for quantifying dissipation in open quantum systems, advancing the understanding of quantum thermodynamics.