AI 中文总结
本研究将双侧玻戈留波夫不等式推广至任意冯·诺依曼代数，获得相对自由能变分表达式，为无限维系统纠缠量化提供了物理合理的热力学判据。
AI 中文摘要
量子力学中的双侧玻戈留波夫不等式为将相互作用粒子系统分离为独立子系统所需的自由能提供上下界，该界可直接通过界面能的系综平均计算，无需直接评估自由能。本研究中，我们利用Araki-Uhlmann相对熵和KMS态的无界微扰理论框架，将双侧玻戈留波夫不等式推广至任意冯·诺依曼代数；此外，我们获得了相对自由能的变分表达式，将现有的有界微扰原理扩展至无界情形。关键的是，这些数学进展为无限维系统中纠缠的量化提供了物理上合理的热力学判据。
英文摘要
The quantum-mechanical two-sided Bogoliubov inequality provides upper and lower bounds for the free energy required to separate a system of interacting particles into independent subsystems. The bounds can be calculated straightforwardly from the ensemble average of the interface energy, bypassing the direct evaluation of the free energy. In this work, we generalize the two-sided Bogoliubov inequality to arbitrary von Neumann algebras by employing the Araki-Uhlmann relative entropy and the framework of unbounded perturbation theory of KMS states. Furthermore, we obtain variational expressions for the relative free energy that extend existing bounded-perturbation principles to the unbounded setting. Crucially, these mathematical developments yield a physically well-founded thermodynamic criterion for the quantification of entanglement in infinite-dimensional systems.
Comments39 pages, 1 figure. Based on the thesis arXiv:2501.04564
