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A generalised form of time-translation-invariance permits to re-derive the known generic phenomenology of ageing, which arises in classical many-body systems after a quench from an initially disordered system to a temperature $T\leq T_c$,…
Natural selection acts on traits at different scales, often with opposing consequences. This article identifies the particular forces that act at each scale and how those forces combine to determine the overall evolutionary outcome. A…
Diffusion probabilistic models excel at sampling new images from learned distributions. Originally motivated by drift-diffusion concepts from physics, they apply image perturbations such as noise and blur in a forward process that results…
Many systems of interest exhibit nested emergent layers with their own rules and regularities, and our knowledge about them seems naturally organised around these levels. This paper proposes that this type of hierarchical emergence arises…
We present a mathematical theory of dynamical fluctuations for the hard sphere gas in the Boltzmann-Grad limit. We prove that: (1) fluctuations of the empirical measure from the solution of the Boltzmann equation, scaled with the square…
Recently, Portelli et al (2003) have semi-numerically obtained a functional form of the probability distribution of fluctuations in the total energy flow in a model for fluid turbulence. This follows earlier work suggesting that…
This study establishes a universal mechanism for entropy production in isolated quantum systems governed by interactions that induce random-phase fluctuations. By developing a resolvent-based framework, we demonstrate that steady-state…
The frequency and magnitude of weather extreme events have increased significantly during the past few years in response to anthropogenic climate change. However, global statistical characteristics and underlying physical mechanisms are…
In recent years, there has been a growing interest in statistical methods that exhibit robust performance under distribution changes between training and test data. While most of the related research focuses on point predictions with the…
The properties of the normal distribution under linear transformation, as well the easy way to compute the covariance matrix of marginals and conditionals, offer a unique opportunity to get an insight about several aspects of uncertainties…
We introduce a family of scale-invariant entropy statistics derived from logarithmically aggregated distance distributions of point processes, with prime numbers serving as a motivating example. The construction associates to each finite…
Large random matrices appear in different fields of mathematics and physics such as combinatorics, probability theory, statistics, operator theory, number theory, quantum field theory, string theory etc... In the last ten years, they…
Classical gradient systems have a linear relation between rates and driving forces. In generalized gradient systems we allow for arbitrary relations derived from general non-quadratic dissipation potentials. This paper describes two natural…
Multifractal systems usually have singularity spectra defined on bounded sets of H\"older exponents. As a consequence, their associated multifractal scaling exponents are expected to depend linearly upon statistical moment orders at high…
A consistent generalization of statistical mechanics is obtained by applying the maximum entropy principle to a trace-form entropy and by requiring that physically motivated mathematical properties are preserved. The emerging…
Sampling a probability distribution with an unknown normalization constant is a fundamental problem in computational science and engineering. This task may be cast as an optimization problem over all probability measures, and an initial…
We show that the statistics of tunnelling can be dramatically affected by scarring and derive distributions quantifying this effect. Strong deviations from the prediction of random matrix theory can be explained quantitatively by modifying…
We apply the Law of Total Probability to the construction of scale-invariant probability distribution functions (pdfs), and require that probability measures be dimensionless and unitless under a continuous change of scales. If the…
The paper assesses stationary probability distributions in out of equilibrium systems. In the phenomenology proposed, no free energy can be well defined. Fluctuations of Landau free energy couplings arise when the intrinsic chemical…
The Weibull distribution can be obtained using a power transformation from the standard exponential distribution. In this article, we will consider a symmetrized power transformation of a random variable with the standard normal…