Related papers: Synergetics and Its Application to Literature and …
Methods and insights from statistical physics are finding an increasing variety of applications where one seeks to understand the emergent properties of a complex interacting system. One such area concerns the dynamics of language at a…
The concept of emergence, or synergy in its simplest form, is widely used but lacks a rigorous definition. Our work connects information and set theory to uncover the mathematical nature of synergy as the failure of distributivity. It…
We present a theoretical and empirical investigation of the statistical behaviour of the words in a text produced by human language. To this aim, we analyse the word distribution of various texts of Italian language selected from a specific…
We model a piece of text of human language telling a story by means of the quantum structure describing a Bose gas in a state close to a Bose-Einstein condensate near absolute zero temperature. For this we introduce energy levels for the…
Quantitative linguistics has been allowed, in the last few decades, within the admittedly blurry boundaries of the field of complex systems. A growing host of applied mathematicians and statistical physicists devote their efforts to…
Fractals, 1/f noise, Zipf's law, and the occurrence of large catastrophic events are typical ubiquitous general empirical observations across the individual sciences which cannot be understood within the set of references developed within…
We show how generalized Gibbs-Shannon entropies can provide new insights on the statistical properties of texts. The universal distribution of word frequencies (Zipf's law) implies that the generalized entropies, computed at the word level,…
The role of background in bosonic quantum statistics is discussed in the frame of a new approach in terms of coherent states. Bosons are indeed detected in different physical situations where they exhibit different and apparently…
This paper presents a geometric approach to the problem of modelling the relationship between words and concepts, focusing in particular on analogical phenomena in language and cognition. Grounded in recent theories regarding geometric…
We checked that the distribution of words in text should uniform, which gives Heaps' law as natural result, that is, the number of types of words can be expressed as a power law of the number of tokens within text. We developed a…
The word-frequency distribution provides the fundamental building blocks that generate discourse in language. It is well known, from empirical evidence, that the word-frequency distribution of almost any text is described by Zipf's law, at…
Inspired by foundational studies in classical and quantum physics, and by information retrieval studies in quantum information theory, we prove that the notions of 'energy' and 'entropy' can be consistently introduced in human language and,…
Zipf's law has been found in many human-related fields, including language, where the frequency of a word is persistently found as a power law function of its frequency rank, known as Zipf's law. However, there is much dispute whether it is…
It turns out that some empirical facts in Big Data are the effects of properties of large numbers. Zipf's law 'noise' is an example of such an artefact. We expose several properties of the power law distributions and of similar distribution…
Zipf's law is a paradigm describing the importance of different elements in communication systems, especially in linguistics. Despite the complexity of the hierarchical structure of language, music has in some sense an even more complex…
Information-theoretic measures such as relative entropy and correlation are extremely useful when modeling or analyzing the interaction of probabilistic systems. We survey the quantum generalization of 5 such measures and point out some of…
We review theoretical results obtained recently in the framework of statistical mechanics to study systems with long range forces. This fundamental and methodological study leads us to consider the different domains of applications in a…
We develop a new master equation as a unified description of the effects of both quantum noise (system-bath interaction) and classical noise on a system's dynamics, using a two-dimensional series expansion method. When quantum and classical…
We provide a brief survey of quantum statistical characterisations of order, disorder and coherence in systems of many degrees of freedom. Here, order and coherence are described in terms of symmetry breakdown, while disorder is described…
Symmetries are playing a very prominent role in natural sciences. In mathematics as the language of physics, symmetries are treated within the framework of group theory, which provides the tools to classify natural laws and physical objects…