Related papers: Comment on "Simple Measure of Complexity"
We respond to the comment by Crutchfield, Feldman and Shalizi and that by Binder and Perry, pointing out that there may be many maximum entropies, and therefore ``disorders'' and ``simple complexities''. Which ones are appropriate depend on…
There is no single universally accepted definition of "Complexity". There are several perspectives on complexity and what constitutes complex behaviour or complex systems, as opposed to regular, predictable behaviour and simple systems. In…
Recently it has been argued that entropy can be a direct measure of complexity, where the smaller value of entropy indicates lower system complexity, while its larger value indicates higher system complexity. We dispute this view and…
The problem of defining and studying complexity of a time series has interested people for years. In the context of dynamical systems, Grassberger has suggested that a slow approach of the entropy to its extensive asymptotic limit is a sign…
The concept of complexity appears in virtually all areas of knowledge. Its intuitive meaning shares similarities across fields, but disagreements between its details hinders a general definition, leading to a plethora of proposed…
The question What is Complexity? has occupied a great deal of time and paper over the last 20 or so years. There are a myriad different perspectives and definitions but still no consensus. In this paper I take a phenomenological approach,…
This work introduces a complexity measure which addresses some conflicting issues between existing ones by using a new principle - measuring the average amount of symmetry broken by an object. It attributes low (although different)…
We review several statistical complexity measures proposed over the last decade and a half as general indicators of structure or correlation. Recently, Lopez-Ruiz, Mancini, and Calbet [Phys. Lett. A 209 (1995) 321] introduced another…
Complexity is a multi-faceted phenomenon, involving a variety of features including disorder, nonlinearity, and self-organisation. We use a recently developed rigorous framework for complexity to understand measures of complexity. We…
A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…
We bound the number of distinct minimal subsystems of a given transitive subshift of linear complexity, continuing work of Ormes and Pavlov [7]. We also bound the number of generic measures such a subshift can support based on its…
We review possible measures of complexity which might in particular be applicable to situations where the complexity seems to arise spontaneously. We point out that not all of them correspond to the intuitive (or "naive") notion, and that…
Numerous definitions for complexity have been proposed over the last half century, with little consensus achieved on how to use the term. A definition of complexity is supplied here that is closely related to the Kolmogorov Complexity and…
A major challenge of interdisciplinary description of complex system behaviour is whether real systems of higher complexity levels can be understood with at least the same degree of objective, "scientific" rigour and universality as…
Complexity of two-level systems, e.g. spins, qubits, magnetic moments etc, are analysed based on the so-called correlational entropy in the case of pure quantum systems and the thermal entropy in case of thermal equilibrium that are…
Concepts used in the scientific study of complex systems have become so widespread that their use and abuse has led to ambiguity and confusion in their meaning. In this paper we use information theory to provide abstract and concise…
The relational complexity, introduced by G. Cherlin, G. Martin, and D. Saracino, is a measure of ultrahomogeneity of a relational structure. It provides an information on minimal arity of additional invariant relations needed to turn given…
Complex systems are found in most branches of science. It is still argued how to best quantify their complexity and to what end. One prominent measure of complexity (the statistical complexity) has an operational meaning in terms of the…
An updated review [1] of nonextensive statistical mechanics and thermodynamics is colloquially presented. Quite naturally the possibility emerges for using the value of q-1 (entropic nonextensivity) as a simple and efficient manner to…
In a topological dynamical system the complexity of an orbit is a measure of the amount of information (algorithmic information content) that is necessary to describe the orbit. This indicator is invariant up to topological conjugation. We…