Related papers: Superstatistics, escort distributions, and applica…
A family of replicator-like dynamics, called the escort replicator equation, is constructed using information-geometric concepts and generalized information entropies and diverenges from statistical thermodynamics. Lyapunov functions and…
Superoscillations have roots in various scientific disciplines, including optics, signal processing, radar theory, and quantum mechanics. This intriguing mathematical phenomenon permits specific functions to oscillate at a rate surpassing…
Statistical mechanics is a powerful framework for analyzing optimization yielding analytical results for matching, optimal transport, and other combinatorial problems. However, these methods typically target the zero-temperature limit,…
Plasmas and other systems with long-range interactions are commonly found in non-equilibrium steady states that are outside traditional Boltzmann-Gibbs statistics, but can be described using generalized statistical mechanics frameworks such…
We comment on some open questions and theoretical peculiarities in Tsallis nonextensive statistical mechanics. It is shown that the theoretical basis of the successful Tsallis' generalized exponential distribution shows some worrying…
Superstatistics describes statistical systems that behave like superpositions of different inverse temperatures $\beta$, so that the probability distribution is $p(\epsilon_i) \propto \int_{0}^{\infty} f(\beta) e^{-\beta \epsilon_i}d\beta$,…
A key challenge in complex design problems that permeate science and engineering is the need to balance design objectives for specific design elements or subsystems with global system objectives. Global objectives give rise to competing…
Within the framework of the random first-order transition theory of glasses, we discuss the statistics of thermal avalanches, the large scale rearrangements in driven amorphous systems near their instability. Stringy excitations yield…
We present an analysis of the stationary distributions of run-and-tumble particles trapped in external potentials in terms of a thermophoretic potential, that emerges when trapped active motion is mapped to trapped passive Brownian motion…
We provide an overview on superstatistical techniques applied to complex systems with time scale separation. Three examples of recent applications are dealt with in somewhat more detail: the statistics of small-scale velocity differences in…
We study dynamical fluctuations in overdamped diffusion processes driven by time periodic forces. This is done by studying fluctuation functionals (rate functions from large deviation theory), of fluctuations around the non-equilibrium…
Cognitive processes undergo various fluctuations and transient states across different temporal scales. Superstatistics are emerging as a flexible framework for incorporating such non-stationary dynamics into existing cognitive model…
This paper is about statistical properties of quasistatic dynamical systems. These are a class of non-stationary systems that model situations where the dynamics change very slowly over time due to external influence. We focus on the case…
This article is an exposition on some recent theoretical advances in learning latent structured models, with a primary focus on the fundamental roles that optimal transport distances play in the statistical theory. We aim at what may be the…
This paper tackles important aspects of comets dynamics from a statistical point of view. Existing methodology uses numerical integration for computing planetary perturbations for simulating such dynamics. This operation is highly…
In this article two models for charges distributions are discussed. On the basis of our consideration we put different points of view for stationary state. We prove that only finite energy model for charges' distribution and well-known…
It is demonstrated that any statistics can be represented by an attractor of the solution to a corresponding systen of ODE coupled with its Liouville equation. Such a non-Newtonian representation allows one to reduce foundations of…
The objective of this work is the investigation of complexity, asymmetry, stochasticity and non-linearity of the financial and economic systems by using the tools of statistical mechanics and information theory. More precisely, this thesis…
The superstatistics concept is a useful statistical method to describe inhomogeneous complex systems for which a system parameter $\beta$ fluctuates on a large spatio-temporal scale. In this paper we analyze a measured time series of wind…
The paper presents some distributional properties of logistic order statistics subject to independent exponential one-sided and two-sided shifts. Utilizing these properties, we extend several known results and obtain some new…