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.

翻译：讨论的是,对有效的Boltzmann因素的超统计性提法如何与科尔莫戈罗夫复杂程度的概念相联系,从而产生一套对信息进行量化的无限的复杂措施(CMs),在这个层次上,信息按其背景处理,这意味着CM取决于信息设想的固有属性。虽然Boltzmann基本因素直接产生标准复杂度(SCM),但它成功地描述了大规模假设,其中数据组成部分彼此不相互关联,从而采用了气体的行为。在不能忽视信息来源和汇的存在的情况下,如果CM是普通的Boltzmann因素产生的,那么CM(CM)需要的除外。我们引入了一套没有自由参数的灵活CMs,它与Kolmogorov复杂程度不相容,同时用合理的小密度来量化假设中的信息。我们证明,这些CMs是从一个一般相对的昆虫获得的。我们建议,为什么这些措施是SCM的唯一兼容性。