相关论文: The Entropy Method in Large Deviation Theory
We study the error introduced by entropy regularization in infinite-horizon discrete discounted Markov decision processes. We show that this error decreases exponentially in the inverse regularization strength, both in a weighted…
We derive a strong law of large numbers, a central limit theorem, a law of the iterated logarithm and a large deviation theorem for so-called deviation means of independent and identically distributed random variables (for the strong law of…
Microscopic formula to describe the entropy of biomolecular solutions are derived based on the Gibbs formula of entropy, and the generalized Langevin theory combined with the RISM/3D-RISM theory. Two formula are derived: one is concerned…
This work analyzes different notions of entropy and its production in $ep$ and heavy-ion collisions, focusing on the early stages of the collision. To this end, the importance of phenomena such as quantum entanglement and decoherence in…
We exploit the idea to use the maximal-entropy method, successfully tested in information theory and statistical thermodynamics, to determine approximating function's coefficients and squared errors' weights simultaneously as output of one…
In this paper we remark that Shannon entropy can be expressed as a function of the self-information (i.e. the logarithm) and the inverse of the Lambert $W$ function. It means that we consider that Shannon entropy has the trace form: $-k…
Entropy stable methods have become increasingly popular in the field of computational fluid dynamics. They often work by satisfying some form of a discrete entropy inequality: a discrete form of the 2nd law of thermodynamics. Schemes which…
Maximum entropy distributions with discrete support in $m$ dimensions arise in machine learning, statistics, information theory, and theoretical computer science. While structural and computational properties of max-entropy distributions…
The ``Gibbs Paradox'' refers to several related questions concerning entropy in thermodynamics and statistical mechanics: whether it is an extensive quantity or not, how it changes when identical particles are mixed, and the proper way to…
Entropy stabilization of the compressible Euler system is achieved by adapting the averages that are applied to the density and internal energy variables. The approach achieves non-linear robustness despite the use of simplified symmetric…
In this article we describe the applications of the relative entropy framework. In particular uniqueness of an entropy solution is proven for a scalar conservation law, using the notion of measure-valued entropy solutions. Further we survey…
The notion of slow entropy, both upper and lower slow entropy, was defined by Katok and Thouvenot as a more refined measure of complexity for dynamical systems, than the classical Kolmogorov-Sinai entropy. For any subexponential rate…
We present a new methodology for the characterization of the metric entropy of infinite-dimensional ellipsoids with exponentially decaying semi-axes. This procedure does not rely on the explicit construction of coverings or packings and…
Information theory on a time-discrete setting in the framework of time series analysis is generalized to the time-continuous case. Considerations of the Roessler and Lorenz dynamics as well as the Ornstein-Uhlenbeck process yield for…
Neural networks have dramatically increased our capacity to learn from large, high-dimensional datasets across innumerable disciplines. However, their decisions are not easily interpretable, their computational costs are high, and building…
We establish a link between the phenomenon of Taylor dispersion and the theory of empirical distributions. Using this connection, we derive, upon applying the theory of large deviations, an alternative and much more precise description of…
The 1D Mueller dipole model, its high energy limit, and its generalization were investigated. To address the ambiguity stemming from different definitions of the pseudorapidity ranges in experimental measurements, we propose the entropy as…
We obtain the large deviation function for entropy production of the medium and its distribution function for two-site totally asymmetric simple exclusion process(TASEP) and three-state unicyclic network. Since such systems are described…
Maximum entropy approach to classification is very well studied in applied statistics and machine learning and almost all the methods that exists in literature are discriminative in nature. In this paper, we introduce a maximum entropy…
Although neural networks can solve very complex machine-learning problems, the theoretical reason for their generalizability is still not fully understood. Here we use Wang-Landau Mote Carlo algorithm to calculate the entropy (logarithm of…