区分图和图熵：经典和量子熵、观测语义学和认知计算的形式化现象层
Distinction Graphs and Graphtropy: A Formalized Phenomenological Layer Underlying Classical and Quantum Entropy, Observational Semantics and Cognitive Computation
摘要：
一个新的概念基础的概念，“信息”的基础上提出了一个“区别图”的概念：一个图，其中两个节点连接，如果他们不能区分由一个特定的观察者。区分图的“图熵”被定义为两个节点的平均连接概率;在区分图由完全连接的子图组成的情况下，这相当于Ellerman的逻辑熵，它与香农熵有直接的关系。概率区分图和概率图熵也被认为是，以及图熵和热力学和量子熵之间的连接。热力学第二定律和最大熵产生原理的语义以一种新颖的方式展开，通过分析区分图的认知过程。这引起了一种解释，其中复杂智能被视为对应于具有中间图熵的意识状态，这与违反导致推导第二定律的假设的记忆缺陷有关。在区分图的节点由可计算实体标记的情况下，图熵被示出为与节点的平均算法信息（相对于观察者的算法信息）单调相关。考虑了量子力学版本的区别图，其中区别可以存在于叠加态中;这产生了图熵作为混合态杂质的度量，并产生了“quangraphtropy”的概念。最后，一个新的计算模型称为动态区分图（DDGs）制定，通过增强区别图与额外的链接表示因果关系的影响，使一个基于区别的模型的“观察者”。"
英文摘要：
A new conceptual foundation for the notion of "information" is proposed, based on the concept of a "distinction graph": a graph in which two nodes are connected iff they cannot be distinguished by a particular observer. The "graphtropy" of a distinction graph is defined as the average connection probability of two nodes; in the case where the distinction graph is a composed of disconnected components that are fully connected subgraphs, this is equivalent to Ellerman's logical entropy, which has straightforward relationships to Shannon entropy. Probabilistic distinction graphs and probabilistic graphtropy are also considered, as well as connections between graphtropy and thermodynamic and quantum entropy. The semantics of the Second Law of Thermodynamics and the Maximum Entropy Production Principle are unfolded in a novel way, via analysis of the cognitive processes underlying the making of distinction graphs This evokes an interpretation in which complex intelligence is seen to correspond to states of consciousness with intermediate graphtropy, which are associated with memory imperfections that violate the assumptions leading to derivation of the Second Law. In the case where nodes of a distinction graph are labeled by computable entities, graphtropy is shown to be monotonically related to the average algorithmic information of the nodes (relative to to the algorithmic information of the observer). A quantum-mechanical version of distinction graphs is considered, in which distinctions can exist in a superposed state; this yields to graphtropy as a measure of the impurity of a mixed state, and to a concept of "quangraphtropy." Finally, a novel computational model called Dynamic Distinction Graphs (DDGs) is formulated, via enhancing distinction graphs with additional links expressing causal implications, enabling a distinction-based model of "observers."
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