Atomic and Laser Physics, Clarendon Laboratory, University of Oxford, Parks Road, Oxford, OX1 3PU, UK.
Centre for Quantum Technologies, National University of Singapore, 117543, Singapore.
Sci Rep. 2017 Mar 7;7:44066. doi: 10.1038/srep44066.
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.
统计力学中的一个关键点是热平衡概念的定义，在某些约束条件下，可以将其定义为最大冯·诺依曼熵的状态。本文认为，这种概念永远无法通过实验来探测，因此我们提出了一种新的热平衡概念，该概念侧重于可观测量，而不是量子系统的完整状态。我们通过最大化其香农熵来描述任意可观测量的这种热平衡概念，并揭示其预示的热性质。我们研究并理解了这种平衡概念与吉布斯系综之间的关系。我们将这种平衡概念应用于一个封闭的量子系统，并表明总是存在一类可观测量表现出热平衡性质，我们给出了一种显式构造它们的方法。最终，揭示了与本征态热化假设的密切联系。
