Thermodynamic Semirings
Thermodynamic Semirings
复制标题
热力学半环
DOI：
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发表时间：
2011
期刊：
影响因子：
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通讯作者：
Ryan Thorngren
中科院分区：
文献类型：
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作者：
M. Marcolli;Ryan Thorngren
Witt结构描述了从环范畴到特征0环范畴的函子。它是由几个关联性约束唯一确定的，这些约束不依赖于所考虑的变量的类型，换句话说，由整数多项式确定。这种普遍性使得Alain Connes和Caterina Consani为特征一设计了一个类似的Witt环，这是一项有吸引力的努力，因为我们对这个奇异特征及其与一个元素对应的领域中的算术知之甚少。有趣的是，他们发现，在特征一中，Witt结构严重依赖于Shannon熵。在目前的工作中，我们研究了这一令人惊讶的现象，定义了任意信息度量的Witt算子和相应的代数，我们称之为热力学半环。这个对象在代数上展示了许多熟悉的信息度量的性质，我们特别研究了Tsallis和Renyi熵函数以及在非广泛热力学和多重分形中的应用。我们发现，热力学半环的算法正是利用给定的信息度量进行的某种猜想游戏的算法。
The Witt construction describes a functor from the category of Rings to the category of characteristic 0 rings. It is uniquely determined by a few associativity constraints which do not depend on the types of the variables considered, in other words, by integer polynomials. This universality allowed Alain Connes and Caterina Consani to devise an analogue of the Witt ring for characteristic one, an attractive endeavour since we know very little about the arithmetic in this exotic characteristic and its corresponding field with one element. Interestingly, they found that in characteristic one, the Witt construction depends critically on the Shannon entropy. In the current work, we examine this surprising occurrence, defining a Witt operad for an arbitrary information measure and a corresponding algebra we call a thermodynamic semiring. This object exhibits algebraically many of the familiar properties of information measures, and we examine in particular the Tsallis and Renyi entropy functions and applications to nonextensive thermodynamics and multifractals. We find that the arithmetic of the thermodynamic semiring is exactly that of a certain guessing game played using the given information measure.
影响因子：
2.7
作者：
Baez, John C.;Fritz, Tobias;Leinster, Tom
通讯作者：
Leinster, Tom