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In a thermodynamic process with measurement and feedback, the second law of thermodynamics is no longer valid. In its place, various second-law-like inequalities have been advanced that each incorporate a distinct additional term accounting…
An important body of quantitative linguistics is constituted by a series of statistical laws about language usage. Despite the importance of these linguistic laws, some of them are poorly formulated, and, more importantly, there is no…
There is a vast body of recent literature on the reliability of communication through noisy channels, the recovery of community structures in the stochastic block model, the limiting behavior of the free entropy in spin glasses and the…
Statistical regularities in human language have fascinated researchers for decades, suggesting deep underlying principles governing its evolution and information structuring for efficient communication. While Zipf's Law describes the…
Despite its obvious relevance, meaning has been outside most theoretical approaches to information in biology. As a consequence, functional responses based on an appropriate interpretation of signals has been replaced by a probabilistic…
We investigate dimensional reduction, the property that the critical behavior of a system in the presence of quenched disorder in dimension d is the same as that of its pure counterpart in d-2, and its breakdown in the case of the…
The composite particle duality extends the notions of both flux attachment and statistical transmutation in spacetime dimensions beyond 2+1D. It constitutes an exact correspondence that can be understood either as a theoretical framework or…
Turbulence exhibits significant velocity fluctuations even if the scale is much larger than the scale of the energy supply. Since any spatial correlation is negligible, these large-scale fluctuations have many degrees of freedom and are…
Recently, researchers started to pay attention to the detection of temporal shifts in the meaning of words. However, most (if not all) of these approaches restricted their efforts to uncovering change over time, thus neglecting other…
The notion of microscopic state of the system at a given moment of time as a point in the phase space as well as a notion of trajectory is widely used in classical mechanics. However, it does not have an immediate physical meaning, since…
The correspondence principle states that classical mechanics emerges from quantum mechanics in the appropriate limits. However, beyond this heuristic rule, an information-theoretic perspective reveals that classical mechanics is a…
How do words change their meaning? Although semantic evolution is driven by a variety of distinct factors, including linguistic, societal, and technological ones, we find that there is one law that holds universally across five major…
The article presents mathematical generalization of results which originated as solutions of practical problems, in particular, the modeling of transitional processes in electrical circuits and problems of resource allocation. However, the…
Vindicating a sophisticated but non-rigorous physics approach called the cavity method, we establish a formula for the mutual information in statistical inference problems induced by random graphs and we show that the mutual information…
In this paper and a companion paper, we attempt to systematically investigate the possibility that the concept of information may enable a derivation of the quantum formalism from a set of physically comprehensible postulates. To do so, we…
For spin and fermionic systems in any spatial dimension, we establish that the superpolynomial decay behavior of mutual information and conditional mutual information is a universal property of gapped pure- and mixed-state phases; i.e., all…
Referring is one of the most basic and prevalent uses of language. How do speakers choose from the wealth of referring expressions at their disposal? Rational theories of language use have come under attack for decades for not being able to…
Here we describe how some important scaling laws observed in the distribution of languages on Earth can emerge from a simple computer simulation. The proposed language dynamics includes processes of selective geographic colonization,…
Analogies have had and continue to have an important role in the development of theoretical physics. They may start from similarities of physical concepts followed by similarities in the mathematical formalization or it may be a purely…
We discuss several models in order to shed light on the origin of power-law distributions and power-law correlations in financial time series. From an empirical point of view, the exponents describing the tails of the price increments…