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The dynamics of technological, economic and social phenomena is controlled by how humans organize their daily tasks in response to both endogenous and exogenous stimulations. Queueing theory is believed to provide a generic answer to…

Nature and our world have a bias! Roughly $30\%$ of the time the number $1$ occurs as the leading digit in many datasets base $10$. This phenomenon is known as Benford's law and it arrises in diverse fields such as the stock market,…

Murphy's Law is $not$ a law in the formal sense yet popular science often compares it with the Second Law of Thermodynamics as both the statements point toward a more disorganized state with time. In this paper, we first construct a…

We consider the atom-optical delta-kicked accelerator when the initial momentum distribution is symmetric. We demonstrate the existence of quantum-resonant dynamics, and derive analytic expressions for the system evolution. In particular,…

Physical laws for elementary particles can be described by the quantum dynamics equation given a Hamiltonian. The solution are probability amplitudes in Hilbert space that evolve over time. A probability density function over position and…

Software development as done using modern methodologies and source control management systems, has been often established as an example of self-organization, with code growing and evolving organically, through activities that do not stem…

Although entanglement can boost metrological precision beyond the standard quantum limit, the advantage often disappears with particle loss. We demonstrate that scrambling safeguards precision by dispersing information about the encoded…

The Arcsine laws of Brownian motion are a collection of results describing three different statistical quantities of one-dimensional Brownian motion: the time at which the process reaches its maximum position, the total time the process…

We study statistics of the knockout tournament, where only the winner of a fixture progresses to the next. We assign a real number called competitiveness to each contestant and find that the resulting distribution of prize money follows a…

The exponential factor of Arrhenius satisfactorily quantifies the energetic restriction of chemical reactions but is still awaiting a rigorous basis. Assuming that the Arrhenius equation should be based on statistical mechanics and is…

Many mathematical, man-made and natural systems exhibit a leading-digit bias, where a first digit (base 10) of 1 occurs not 11\% of the time, as one would expect if all digits were equally likely, but rather 30\%. This phenomenon is known…

Repeated measurements as typically occurring in two- or multi-time correlators rely on von Neumann's projection postulate, telling how to restart the system after an intermediate measurement. We invoke the principle of deferred measurement…

Quantum mechanics---the theory describing the fundamental workings of nature---is famously counterintuitive: it predicts that a particle can be in two places at the same time, and that two remote particles can be inextricably and…

Scaling laws, a defining feature of deep learning, reveal a striking power-law improvement in model performance with increasing dataset and model size. Yet, their mathematical origins, especially the scaling exponent, have remained elusive.…

We present the data on wealth and income distributions in the United Kingdom, as well as on the income distributions in the individual states of the USA. In all of these data, we find that the great majority of population is described by an…

We report an empirical determination of the probability density functions P(r) of the number r of earthquakes in finite space-time windows for the California catalog, over fixed spatial boxes 5 x 5 km^2 and time intervals dt =1, 10, 100 and…

Language models famously improve under a smooth scaling law, but some specific capabilities exhibit sudden breakthroughs in performance. Advocates of "emergence" view these capabilities as unlocked at a specific scale, but others attribute…

A quantum walker moves on the integers with four extra degrees of freedom, performing a coin-shift operation to alter its internal state and position at discrete units of time. The time evolution is described by a unitary process. We focus…

For those concerned with the long-term value of their accounts, it can be a challenge to plan in the present for inflation-adjusted economic growth over coming decades. Here, I argue that there exists an economic constant that carries…

Quantum scrambling describes the spreading of local information into many degrees of freedom in quantum systems. This provides the conceptual connection among diverse phenomena ranging from thermalizing quantum dynamics to models of black…