复杂性测度的超统计公式
A superstatistical formulation of complexity measures
摘要：
它讨论了如何有效玻尔兹曼因子的超统计公式可以与柯尔莫哥洛夫复杂性的概念，产生一个无限集的复杂性措施（CM）的量化信息。在这个层次上，信息是根据其背景来处理的，这意味着CM取决于信息场景的固有属性。虽然基本玻尔兹曼因子直接产生标准复杂性度量（SCM），但它成功地描述了大规模场景，其中数据组件与自身不相关，从而采用了气体的行为。发生了什么情况下，其中存在的源和汇的信息不能被忽略，需要CM以外的普通玻尔兹曼因素产生的。我们引入了一组灵活的CM，没有自由参数，渐近收敛到Kolmogorov复杂性，但也量化的情况下，一个合理的小密度的状态的信息。我们证明，这些CM是从广义相对熵，我们建议为什么这样的措施是唯一兼容的概括SCM。
英文摘要：
It is discussed how the superstatistical formulation of effective Boltzmann factors can be related to the concept of Kolmogorov complexity, generating an infinite set of complexity measures (CMs) for quantifying information. At this level, the information is treated according to its background, which means that the CM depends on the inherent attributes of the information scenario. While the basic Boltzmann factor directly produces the standard complexity measure (SCM), it succeeds in the description of large-scale scenarios where the data components are not interrelated with themselves, thus adopting the behaviour of a gas. What happens in scenarios in which the presence of sources and sinks of information cannot be neglected, needs of a CM other than the one produced by the ordinary Boltzmann factor. We introduce a set of flexible CMs, without free parameters, that converge asymptotically to the Kolmogorov complexity, but also quantify the information in scenarios with a reasonable small density of states. We prove that these CMs are obtained from a generalised relative entropy and we suggest why such measures are the only compatible generalisations of the SCM.
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