Related papers: Statistical Laws in Complex Systems
The record statistics of complex random states are analytically calculated, and shown that the probability of a record intensity is a Bernoulli process. The correlation due to normalization leads to a probability distribution of the records…
Within the continuous endeavour of improving the efficiency and resilience of air transport, the trend of using concepts and metrics from statistical physics has recently gained momentum. This scientific discipline, which integrates…
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…
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 power law is ubiquitous in natural and social phenomena, and is considered as a universal relationship between the frequency and its rank for diverse social systems. However, a general model is still lacking to interpret why these…
There is no compelling reason imposing that the methods of statistical mechanics should be restricted to the dynamical systems which follow the usual Boltzmann-Gibbs prescriptions. More specifically, ubiquitous natural and artificial…
General characterizations of physical measurements are discussed within the framework of the classical information theory. The uncertainty relation for simultaneous measurements of two physical observables is defined in this framework for…
The study of complex systems is limited by the fact that only few variables are accessible for modeling and sampling, which are not necessarily the most relevant ones to explain the systems behavior. In addition, empirical data typically…
Statistical physics and dynamical systems theory are key tools to study high-impact geophysical events such as temperature extremes, cyclones, thunderstorms, geomagnetic storms and many more. Despite the intrinsic differences between these…
A statistical model for describing the scaling of the distribution of inter-event times is described. By considering the diverse region seismicity (natural and induced) at different scale levels the self-similarity of the distribution has…
Deep learning has recently revealed the existence of scaling laws, demonstrating that model performance follows predictable trends based on dataset and model sizes. Inspired by these findings and fascinating phenomena emerging in the…
In a language corpus, the probability that a word occurs $n$ times is often proportional to $1/n^2$. Assigning rank, $s$, to words according to their abundance, $\log s$ vs $\log n$ typically has a slope of minus one. That simple Zipf's law…
Informatics and technological advancements have triggered generation of huge volume of data with varied complexity in its management and analysis. Big Data analytics is the practice of revealing hidden aspects of such data and making…
We study a few dynamical systems composed of many components whose sizes evolve according to multiplicative stochastic rules. We compare them with respect to the emergence of power laws in the size distribution of their components. We show…
Large language models with a huge number of parameters, when trained on near internet-sized number of tokens, have been empirically shown to obey neural scaling laws: specifically, their performance behaves predictably as a power law in…
Statistical mechanics relies on the complete though probabilistic description of a system in terms of all the microscopic variables. Its object is to derive therefrom static and dynamic properties involving some reduced set of variables.…
Uncovering the mechanism leading to the scaling law in human trajectories is of fundamental importance in understanding many spatiotemporal phenomena. We propose a hierarchical geographical model to mimic the real traffic system, upon which…
Identical systems, or entities, are indistinguishable in quantum mechanics (QM), and the symmetrization postulate rules the possible statistical distributions of a large number of identical quantum entities. However, a thorough analysis on…
When the probability of measuring a particular value of some quantity varies inversely as a power of that value, the quantity is said to follow a power law, also known variously as Zipf's law or the Pareto distribution. Power laws appear…
Scaling laws illuminate Nature's fundamental biological principles and guide bioinspired materials and structural designs. In simple cases they are based on the fundamental principle that all laws of nature remain unchanged (i.e.,…