相关论文: Generalized Entropy Method for the Renewal Equatio…
This thesis synthesizes probability and entropic inference with Quantum Mechanics (QM) and quantum measurement [1-6]. It is shown that the standard and quantum relative entropies are tools designed for the purpose of updating probability…
Entropy is useful in statistical problems as a measure of irreversibility, randomness, mixing, dispersion, and number of microstates. However, there remains ambiguity over the precise mathematical formulation of entropy, generalized beyond…
A novel heuristic approach is proposed here for time series data analysis, dubbed Generalized weighted permutation entropy, which amalgamates and generalizes beyond their original scope two well established data analysis methods:…
Quantum information-theoretic approach has been identified as a way to understand the foundations of quantum mechanics as early as 1950 due to Shannon. However there hasn't been enough advancement or rigorous development of the subject. In…
We demonstrate how information in the form of observable data and moment constraints are introduced into the method of Maximum relative Entropy (ME). A general example of updating with data and moments is shown. A specific econometric…
The study considers advantages of the introduced measure of time based on the entropy change under irreversible processes (entropy production). Using the example of non-equilibrium expansion of an ideal gas in vacuum, such a measure is…
General hyperbolic systems of balance laws with inhomogeneity in space and time in all constitutive functions are studied in the context of relative entropy. A framework is developed in this setting that contributes to a measure-valued weak…
We describe an approach to improving model fitting and model generalization that considers the entropy of distributions of modelling residuals. We use simple simulations to demonstrate the observational signatures of overfitting on ordered…
The problem of assigning probability distributions which objectively reflect the prior information available about experiments is one of the major stumbling blocks in the use of Bayesian methods of data analysis. In this paper the method of…
Relative entropy is a measure of distinguishability for quantum states, and plays a central role in quantum information theory. The family of Renyi entropies generalizes to Renyi relative entropies that include as special cases most entropy…
We study the problem of detecting the structure of a complex dynamical system described by a set of deterministic differential equation that contains a Hamiltonian subsystem, without any information on the explicit form of evolution laws.…
As a part of the construction of an information theory based on general probabilistic theories, we propose and investigate the several distinguishability measures and "entropies" in general probabilistic theories. As their applications,…
We find that the standard relative entropy and the Umegaki entropy are designed for the purpose of inferentially updating probability and density matrices respectively. From the same set of inferentially guided design criteria, both of the…
By virtue of the generalized Hellmann-Feynman theorem for ensemble average, we obtain internal energy and average energy consumed by the resistance R in a quantized RLC electric circuit. We also calculate entropy-variation with respect to…
We present a new type of generalization of the Renyi entropy that follows naturally from its representation as a thermodynamic quantity. We apply it to the case of d-dimensional conformal field theories (CFTs) reduced on a region bounded by…
The relative entropy for two different degenerate diffusion processes is estimated by using the Wasserstein distance of initial distributions and the difference between coefficients. As applications, the entropy cost inequality and…
Entropy is a measure of self-information which is used to quantify losses. Entropy was developed in thermodynamics, but is also used to compare probabilities based on their deviating information content. Corresponding model uncertainty is…
This research paper delves into the innovative integration of Shannon entropy and rough set theory, presenting a novel approach to generalize the evaluation approach in machine learning. The conventional application of entropy, primarily…
The interrelationships of the fundamental biological processes natural selection, mutation, and stochastic drift are quantified by the entropy rate of Moran processes with mutation, measuring the long-run variation of a Markov process. The…
The fermionic relative entropy in two-dimensional Rindler spacetime is studied using both modular theory and the reduced one-particle density operators. The methods and results are compared. A formula for the relative entropy for general…