Information-theoretic equilibrium and observable thermalization
Information-theoretic equilibrium and observable thermalization
复制标题
信息论平衡和可观测热化
作者：
Fabio Anza;V. Vedral
统计力学的一个关键点是热平衡概念的定义，可以将其定义为在某些约束的有效性下使冯·诺依曼熵最大化的状态。认为这样的概念永远无法通过实验探测，在本文中，我们提出了一种新的热平衡概念，重点关注可观测值而不是量子系统的完整状态。我们通过香农熵的最大化来描述任意可观察量的热平衡概念，并揭示它所预示的热性质。研究并理解了与吉布斯系综的关系。我们将这种平衡概念应用于封闭的量子系统，并表明总有一类可观测量表现出热平衡性质，并且我们给出了显式构造它们的方法。最终，与本征态热化假说的密切联系被揭示。
A crucial point in statistical mechanics is the definition of the notion of thermal equilibrium, which can be given as the state that maximises the von Neumann entropy, under the validity of some constraints. Arguing that such a notion can never be experimentally probed, in this paper we propose a new notion of thermal equilibrium, focused on observables rather than on the full state of the quantum system. We characterise such notion of thermal equilibrium for an arbitrary observable via the maximisation of its Shannon entropy and we bring to light the thermal properties that it heralds. The relation with Gibbs ensembles is studied and understood. We apply such a notion of equilibrium to a closed quantum system and show that there is always a class of observables which exhibits thermal equilibrium properties and we give a recipe to explicitly construct them. Eventually, an intimate connection with the Eigenstate Thermalisation Hypothesis is brought to light.
DOI：
10.1103/physreve.91.012120
发表时间：
2014-08
期刊：
Physical review. E, Statistical, nonlinear, and soft matter physics
影响因子：
--
作者：
A. Khodja;R. Steinigeweg;J. Gemmer
通讯作者：
A. Khodja;R. Steinigeweg;J. Gemmer
影响因子：
8.6
作者：
R. Steinigeweg;Abdelah Khodja;Hendrik Niemeyer;C. Gogolin;J. Gemmer
通讯作者：
R. Steinigeweg;Abdelah Khodja;Hendrik Niemeyer;C. Gogolin;J. Gemmer
影响因子：
3.3
作者：
Reimann, Peter
通讯作者：
Reimann, Peter