Related papers: Orders of Growth and Generalized Entropy
We study a class of generalized expansive dynamical systems for which at most countable orbits can be accompanied by an arbitrary given orbit. Examples of different levels of generalized expansiveness are constructed. When the dynamical…
In this paper, we extend the concept of generalized entropy to uniform spaces, allowing computations beyond metrizable settings. We apply this to parabolic dynamics - systems with a unique fixed point uniformly attracting all compact…
In this article, we study the behaviour of discrete one-dimensional dynamical systems associated to functions on finite sets. We formalise the global orbit pattern formed by all the periodic orbits (gop) as the ordered set of periods when…
In this paper, the study of the global orbit pattern (gop) formed by all the periodic orbits of discrete dynamical systems on a finite set $X$ allows us to describe precisely the behaviour of such systems. We can predict by means of closed…
The concept of entropy connects the number of possible configurations with the number of variables in large stochastic systems. Independent or weakly interacting variables render the number of configurations scale exponentially with the…
Given entropy's central role in multiple areas of physics and science, one important task is to develop a systematic and unifying approach to defining entropy. Games of chance become a natural candidate for characterising the uncertainty of…
For any discrete time dynamical system with a rational evolution, we define an entropy, which is a global index of complexity for the evolution map. We analyze its basic properties and its relations to the singularities and the…
We study the problem of detecting the structure of a complex dynamical system described by a set of deterministic differential equation that contains a Hamiltonian subsystem, without any information on the explicit form of evolution laws.…
The existence of the {\em typical set} is key for data compression strategies and for the emergence of robust statistical observables in macroscopic physical systems. Standard approaches derive its existence from a restricted set of…
We define the class of multivariate group entropies as a novel set of information - theoretical measures, which extends significantly the family of group entropies. We propose new examples related to the "super-exponential" universality…
We present a number of second order maps, which pass the singularity confinement test commonly used to identify integrable discrete systems, but which nevertheless are non-integrable. As a more sensitive integrability test, we propose the…
In the past many papers have appeared which simulated surface growth with different growth models. The results showed that, if models differed only slightly in their `growth' rules, the resulting surfaces may belong to different…
Entropy plays a key role in statistical physics of complex systems, which in general exhibit diverse aspects of emergence on different scales. However, it still remains not fully resolved how entropy varies with the coarse-graining level…
Self-organization is the autonomous assembly of a network of interacting components into a stable, organized pattern. This article shows that the process of self-assembly can be encoded in terms of evolutionary entropy, a statistical…
In this paper we revisit the concept of mobility entropy. Over time, the structure of spatial interactions among urban centres tends to become more complex and evolves from centralised models to more scattered origin and destination…
A large class of technically non-chaotic systems, involving scatterings of light particles by flat surfaces with sharp boundaries, is nonetheless characterized by complex random looking motion in phase space. For these systems one may…
We introduce a solvable model of randomly growing systems consisting of many independent subunits. Scaling relations and growth rate distributions in the limit of infinite subunits are analysed theoretically. Various types of scaling…
The question how complex systems become more organized and efficient with time is open. Examples are, the formation of elementary particles from pure energy, the formation of atoms from particles, the formation of stars and galaxies, the…
In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a…
We construct the generalized entropy optimized by a given arbitrary statistical distribution with a finite linear expectation value of a random quantity of interest. This offers, via the maximum entropy principle, a unified basis for a…