Related papers: Measure Theoretic Aspects Of Error Terms
Fluctuation theorems make use of time reversal to make predictions about entropy production in many-body systems far from thermal equilibrium. Here we review the wide variety of distinct, but interconnected, relations that have been derived…
We study quantum measurements of temporal equilibrium fluctuations in macroscopic quantum systems. It is shown that the fluctuation-dissipation theorem, as a relation between observed quantities, is partially violated in quantum systems,…
At present a number of current or proposed experiments are directed towards a search for a `new physics' by detecting variations of fundamental physical constants or violations of certain basic symmetries. Various problems related to the…
The application of machine learning to physics problems is widely found in the scientific literature. Both regression and classification problems are addressed by a large array of techniques that involve learning algorithms. Unfortunately,…
We discuss various measures of net charge (conserved quantities) fluctuations proposed for the identification of critical phenomena in heavy ion collisions. We show the dynamical component of fluctuations of the net charge can be expressed…
This paper is concerned with the asymptotic behavior of sums of terms which are a test function f evaluated at successive increments of a discretely sampled semimartingale. Typically the test function is a power function (when the power is…
A general self-consistency approach allows a thorough treatment of the corrections to the standard mean-field approximation (MFA). The natural extension of standard MFA with the help of a cumulant expansion leads to a new point of view on…
In this work, I analyze the quantum fluctuations and the thermal fluctuations in the framework of quantum mechanics. Being recognized as incoherent perturbations with different features, fluctuations of these two types lead to dissipative…
The theory of error-correcting codes is concerned with constructing codes that optimize simultaneously transmission rate and relative minimum distance. These conflicting requirements determine an asymptotic bound, which is a continuous…
A mathematical framework for the physics of nonequilibrium phenomena is gradually being developed. This review is meant to shed light on some aspects of Response Theory, on the theory of Fluctuation Relations, on the so-called "t-mixing"…
Tur\'an type inequalities for modified Bessel functions of the first kind are used to deduce some sharp lower and upper bounds for the asymptotic order parameter of the stochastic Kuramoto model. Moreover, approximation from the Lagrange…
Topic models extract representative word sets - called topics - from word counts in documents without requiring any semantic annotations. Topics are not guaranteed to be well interpretable, therefore, coherence measures have been proposed…
It is shown that quantum fluctuation theorems remain unaffected if measurements of any kind and number of observables are performed during the action of a force protocol. That is, although the backward and forward probabilities entering the…
Fluctuation Theorem(FT) has been studied as far from equilibrium theorem, which relates the symmetry of entropy production. To investigate the application of this theorem, especially to biological physics, we consider the FT for tilted…
This article traces the development of fluctuation theory and its deep connection to irreversibility, from equilibrium to near-equilibrium, and finally to far-from-equilibrium systems. Classical fluctuation theorems, which capture the…
The Fluctuation Theorem describes the probability ratio of observing trajectories that satisfy or violate the second law of thermodynamics. It has been proved in a number of different ways for thermostatted deterministic nonequilibrium…
We consider nonparametric testing in a non-asymptotic framework. Our statistical guarantees are exact in the sense that Type I and II errors are controlled for any finite sample size. Meanwhile, one proposed test is shown to achieve minimax…
The energy of a finite system thermally connected to a thermal reservoir may fluctuate, while the temperature is a constant representing a thermodynamic property of the reservoir. The finite system can also be used as a thermometer for the…
In a posteriori error analysis, the relationship between error and estimator is usually spoiled by so-called oscillation terms, which cannot be bounded by the error. In order to remedy, we devise a new approach where the oscillation has the…
In the report the approach to estimation of quality of planned experiments is considered. This approach is based on the analysis of uncertainty, which will take place under the future hypotheses testing about the existence of a new…