公理热力学中的光滑熵
Smooth entropy in axiomatic thermodynamics
摘要：
热力学可以用两种方法中的任何一种来表述，现象学方法，它指的是系统的宏观性质，统计方法，它描述系统的微观成分。我们建立了一个新的公理框架，可以考虑到错误和不精确的这两种方法之间的联系。这种联系延伸到包括微观系统在内的任意大小的系统，对这些系统来说，不精确性的处理与任何现实情况都是相关的。在此基础上，我们确定的数量，证明某些热力学过程是否可能与熵的措施，从信息论。在容错的情况下，这些熵是所谓的平滑最小和最大熵。我们的考虑进一步表明，在一个适当的宏观限制，有一个单一的熵测量，表征哪些状态转换是可能的。在系统的许多独立副本的情况下（所谓的i.i.d. regime），相关的量是冯诺伊曼熵。
英文摘要：
Thermodynamics can be formulated in either of two approaches, the phenomenological approach, which refers to the macroscopic properties of systems, and the statistical approach, which describes systems in terms of their microscopic constituents. We establish a connection between these two approaches by means of a new axiomatic framework that can take errors and imprecisions into account. This link extends to systems of arbitrary sizes including microscopic systems, for which the treatment of imprecisions is pertinent to any realistic situation. Based on this, we identify the quantities that characterise whether certain thermodynamic processes are possible with entropy measures from information theory. In the error-tolerant case, these entropies are so-called smooth min and max entropies. Our considerations further show that in an appropriate macroscopic limit there is a single entropy measure that characterises which state transformations are possible. In the case of many independent copies of a system (the so-called i.i.d. regime), the relevant quantity is the von Neumann entropy.
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