论文标题
熵和可逆催化
Entropy and reversible catalysis
论文作者
论文摘要
我表明，非额定熵提供了一种必要和充分的条件，可以通过对感兴趣系统的可逆转换和进一步的“催化剂”的状态将物理系统的状态转换为另一个状态，其状态必须在过渡中完全不变。在有限维量子力学的情况下，该陈述既证明了这一点，否则von〜neumann熵是相关的熵，并且在系统的情况下，该状态是由有限样品空间上的概率分布描述的，那里的香农熵是相关的熵。结果给出了Boes等人引入的（近似）“催化熵猜想”的肯定解决方案。 [PRL 122，210402（2019）]。它们提供了完整的单次表征，而没有冯·诺伊曼熵和香农熵的外部随机性。我还将结果与现象学热力学的设置进行了比较，并展示了如何用于在量子统计力学中获得吉布斯态的定量单拍表征。
I show that non-decreasing entropy provides a necessary and sufficient condition to convert the state of a physical system into a different state by a reversible transformation that acts on the system of interest and a further "catalyst" whose state has to remain invariant exactly in the transition. This statement is proven both in the case of finite-dimensional quantum mechanics, where von~Neumann entropy is the relevant entropy, and in the case of systems whose states are described by probability distributions on finite sample spaces, where Shannon entropy is the relevant entropy. The results give an affirmative resolution to the (approximate) "catalytic entropy conjecture" introduced by Boes et al. [PRL 122, 210402 (2019)]. They provide a complete single-shot characterization without external randomness of von Neumann entropy and Shannon entropy. I also compare the results to the setting of phenomenological thermodynamics and show how they can be used to obtain a quantitative single-shot characterization of Gibbs states in quantum statistical mechanics.
