Related papers: Stability criteria for q-expectation values
Stable quantum computation requires noisy results to remain bounded even in the presence of noise fluctuations. Yet non-stationary noise processes lead to drift in the varying characteristics of a quantum device that can greatly influence…
Throughout quantum mechanics there is statistical balance, in the collective response of an ensemble of systems to differing measurement types. Statistical balance is a core feature of quantum mechanics, underlying quantum mechanical…
Impulsive systems are a very flexible class of systems that can be used to represent switched and sampled-data systems. We propose to extend here the previously obtained results on deterministic impulsive systems to the stochastic setting.…
In probability theory, there is a tendency to treat one random variable with a given distribution as being just as good as any other. By and large this is fine because probability is (mostly) concerned with distributional properties of…
Reliable uncertainty quantification (UQ) in machine learning (ML) regression tasks is becoming the focus of many studies in materials and chemical science. It is now well understood that average calibration is insufficient, and most studies…
Quantum theory is formulated as the only consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if there are two different ways to compute an amplitude the two answers must agree. This…
The concept of Jeans gravitational instability is rediscussed in the framework of nonextensive statistics and its associated kinetic theory. A simple analytical formula generalizing the Jeans criterion is derived by assuming that the…
In this work, we explore both the ordinary $q$-Gaussian distribution and a new one defined here, determining both their mean and variance, and we use them to construct solutions of the $q$-deformed diffusion differential equation. This…
The non-equilibrium steady states emerging from stochastic resetting to a distribution is studied. We show that for a range of processes, the steady-state moments can be expressed as a linear combination of the moments of the distribution…
In this paper, a unified mathematical expression for the constraints leading to the equilibrium distributions of both extensive and non-extensive systems is presented. Based on this expression, a recommendation is made to replace Tsallis'…
Consider bivariate observations $(X_1,Y_1), \ldots, (X_n,Y_n) \in \mathbb{R}\times \mathbb{R}$ with unknown conditional distributions $Q_x$ of $Y$, given that $X = x$. The goal is to estimate these distributions under the sole assumption…
Nonextensive quantum gas distributions are investigated on the basis of the factorization hypothesis of compound probability required by thermodynamic equilibrium. It is shown that the formalisms of Tsallis nonextensive statistical…
An input-output approach to stability analysis is explored for networked systems with uncertain link dynamics. The main result consists of a collection of integral quadratic constraints, which together imply robust stability of the…
The stability of the Standard Model is determined by the true minimum of the effective Higgs potential. We show that the potential at its minimum when computed by the traditional method is strongly dependent on the gauge parameter. It…
When a system has more than one stable state, how can the stability of these states be compared? This deceptively simple question has important consequences for ecosystems, because systems with alternative stable states can undergo dramatic…
We study the properties of Q-balls dominated by the thermal logarithmic potential analytically instead of estimating the characters with only some specific values of model variables numerically. In particular the analytical expressions for…
We consider different models of stochastic dissipative equations and theoretically compute the probability distribution functions (actually the associated large deviation functions) of the time averaged injected power required to sustain a…
We find a general formula for the distribution of time averaged observables for weakly non-ergodic systems. Such type of ergodicity breaking is known to describe certain systems which exhibit anomalous fluctuations, e.g. blinking quantum…
Stochastic differential equations have proved to be a valuable governing framework for many real-world systems which exhibit ``noise'' or randomness in their evolution. One quality of interest in such systems is the shape of their…
The sub-Gaussian stable distribution is a heavy-tailed elliptically contoured law which has interesting applications in signal processing and financial mathematics. This work addresses the problem of feasible estimation of distributions. We…