Related papers: Links between Entropy, Complexity, and the Technol…
From bird flocking to neural dynamics, complex systems generate fascinating structures and correlations. Often, seemingly simple dynamics lead to intricate emergent properties. Despite their visceral appeal, defining complex systems lacks…
In a recent paper Andrei N. Soklakov explained the foundations of the Lagrangian formulation of classical particle mechanics by means of Kolmogorov complexity. In the present paper we use some of Soklakov ideas in order to derive the second…
We introduce two numerical conjugacy invariants for dynamical systems -- the complexity and weak complexity indices -- which are well-suited for the study of "completely integrable" Hamiltonian systems. These invariants can be seen as "slow…
Neural networks have dramatically increased our capacity to learn from large, high-dimensional datasets across innumerable disciplines. However, their decisions are not easily interpretable, their computational costs are high, and building…
Transitivity, the existence of periodic points and positive topological entropy can be used to characterize complexity in dynamical systems. It is known that for graphs that are not trees, for every $\varepsilon>0,$ there exist (complicate)…
Quantum complexity is emerging as a key property of many-body systems, including black holes, topological materials, and early quantum computers. A state's complexity quantifies the number of computational gates required to prepare the…
The relationship between entropy and information is reviewed, taking into account that information is stored in macroscopic degrees of freedom, such as the order parameter in a system exhibiting spontaneous symmetry breaking. It is shown…
We first show how a new definition of entropy, which is intuitively very simple, as a divergence in cluster-size space, leads to a generalized form that is nonextensive for correlated units, but coincides exactly with the conventional one…
We derive an optimal bound on the sum of entropic uncertainties of two or more observables when they are sequentially measured on the same ensemble of systems. This optimal bound is shown to be greater than or equal to the bounds derived in…
The concept of entropy in nonequilibrium macroscopic systems is investigated in the light of an extended equation of motion for the density matrix obtained in a previous study. It is found that a time-dependent information entropy can be…
Knowhow in societies accumulates as it gets transmitted from group to group, and from generation to generation. However, we lack of a unified quantitative formalism that takes into account the structured process for how this accumulation…
In closed quantum many-body systems, initially localized information spreads throughout the system and becomes highly complex. This phenomenon, known as information scrambling, is closely related to entropy growth and quantum…
The entropy of network ensembles characterizes the amount of information encoded in the network structure, and can be used to quantify network complexity, and the relevance of given structural properties observed in real network datasets…
Even today, the concept of entropy is perceived by many as quite obscure. The main difficulty is analyzed as being fundamentally due to the subjectivity and anthropocentrism of the concept that prevent us to have a sufficient distance to…
The defining property of an artificial physical self-replicating system, such as a self-replicating robot, is that it has the ability to make copies of itself from basic parts. Three questions that immediately arises in the study of such…
Information plays an important role in our understanding of the physical world. We hence propose an entropic measure of information for any physical theory that admits systems, states and measurements. In the quantum and classical world,…
The emergence of a complex, large-scale organisation of cosmic matter into the Cosmic Web is a beautiful exemplification of how complexity can be produced by simple initial conditions and simple physical laws. In the epoch of Big Data in…
Technological cumulativeness is considered one of the main mechanisms for technological progress, yet its exact meaning and dynamics often remain unclear. To develop a better understanding of this mechanism we approach a technology as a…
These lectures deal with the problem of inductive inference, that is, the problem of reasoning under conditions of incomplete information. Is there a general method for handling uncertainty? Or, at least, are there rules that could in…
It has been demonstrated that excitable media with a tree structure performed better than other network topologies, it is natural to consider neural networks defined on Cayley trees. The investigation of a symbolic space called tree-shift…