Related papers: The Significant Digit Law in Statistical Physics
We consider the continued fraction digits as random variables measured with respect to Lebesgue measure. The logarithmically scaled and normalized fluctuation process of the digit sums converges strongly distributional to a random variable…
A curious observation was made that the rank statistics of scientific citation numbers follows Zipf-Mandelbrot's law. The same pow-like behavior is exhibited by some simple random citation models. The observed regularity indicates not so…
In this second part of our survey on the social and natural distributions, we investigate some models, which intend to explain the statistical regularity of the natural and social distributions. There is a large variety of models and in…
For the first time, we introduce "Scaling invariable Benford distance" and "Benford cyclic graph", which can be used to analyze any data set. Using the quantity and the graph, we analyze some date sets with common distributions, such as…
The Boltzmann distribution (the most probable distribution) is one of the most important concepts used in physics, chemistry and biology. Suppose we put the system initially in one of the less probable state then the system will find the…
The yearly aggregated tax income data of all, more than 8000, Italian municipalities are analyzed for a period of five years, from 2007 to 2011, to search for conformity or not with Benford's law, a counter-intuitive phenomenon observed in…
An important aspect of religious association is that adherents, as part of their religious duty, carry out various activities. One religious group known for keeping the elaborate records of day-to-day activities of its members is the…
In this paper, we show two kinds of entangled many body systems with special statistic properties. Firstly, an entangled fermions system with a pairwise entanglement between every two particles in the lowest energy energy level obeys the…
This article presents a modern deterministic framework for the study of leading significant digit distributions in numerical data. Rather than relying on traditional probabilistic or mixture-based explanations, we demonstrate that the…
Benford's law is often used as a support to critical decisions related to data quality or the presence of data manipulations or even fraud. However, many authors argue that conventional statistical tests will reject the null of data…
We study the individual digits for the absolute value of the characteristic polynomial for the Circular $\beta$-Ensemble. We show that, in the large $N$ limit, the first digits obey Benford's Law and the further digits become uniformly…
A weak law of large numbers is established for a sequence of systems of N classical point particles with logarithmic pair potential in $\bbR^n$, or $\bbS^n$, $n\in \bbN$, which are distributed according to the configurational microcanonical…
Recent research on the fundamentals of statistical mechanics has led to an interesting discovery [1-3]: With locally nonchaotic barriers, as Boltzmann's H-theorem is inapplicable, there exist nontrivial non-thermodynamic systems that can…
The cornerstone of Boltzmann-Gibbs ($BG$) statistical mechanics is the Boltzmann-Gibbs-Jaynes-Shannon entropy $S_{BG} \equiv -k\int dx f(x)\ln f(x)$, where $k$ is a positive constant and $f(x)$ a probability density function. This theory…
A general statistical thermodynamic theory that considers given sequences of x-integers to play the role of particles of known type in an isolated elastic system is proposed. By also considering some explicit discrete probability…
The \textit{ternary digits of $2^n$} are a finite sequence of 0s, 1s, and 2s. It is a natural question to ask whether the frequency of any string of 0s, 1s, and 2s in this sequence approaches the same limit for all strings of the same…
The normal distribution is used as a unified probability distribution, however, our researcher found that it is not good agreed with the real-life dynamical system's data. We collected and analyzed representative naturally occurring data…
The negative binomial distribution (NBD) has been theorized to express a scale-invariant property of many-body systems and has been consistently shown to outperform other statistical models in both describing the multiplicity of…
Physics seeks to uncover the laws of Nature and express them through mathematical equations. Despite the vast diversity of natural phenomena, physical equations exhibit structural regularities that set them apart from arbitrary mathematical…
Fibonacci numbers and the golden ratio can be found in nearly all domains of Science, appearing when self-organization processes are at play and/or expressing minimum energy configurations. Several non-exhaustive examples are given in…