287,557 research outputs found
Entropy and Entropy Production in Some Applications
By using entropy and entropy production, we calculate the steady flux of some
phenomena. The method we use is a competition method, , where is system entropy, is entropy production and
is microscopic interaction time. System entropy is calculated from the
equilibrium state by studying the flux fluctuations. The phenomena we study
include ionic conduction, atomic diffusion, thermal conduction and viscosity of
a dilute gas
Generalized maximum entropy (GME) estimator: formulation and a monte carlo study
The origin of entropy dates back to 19th century. In 1948, the entropy concept as a measure of uncertainty was developed by Shannon. A decade after in 1957, Jaynes formulated Shannonâs entropy as a method for estimation and inference particularly for ill-posed problems by proposing the so called Maximum Entropy (ME) principle. More recently, Golan et al. (1996) developed the Generalized Maximum Entropy (GME) estimator and started a new discussion in econometrics. This paper is divided into two parts. The first part considers the formulation of this new technique (GME). Second, by Monte Carlo simulations the estimation results of GME will be discussed in the context of non-normal disturbances.Entropy, Maximum Entropy, ME, Generalized Maximum Entropy, GME, Monte Carlo Experiment, Shannonâs Entropy, Non-normal disturbances
Updating Probabilities
We show that Skilling's method of induction leads to a unique general theory
of inductive inference, the method of Maximum relative Entropy (ME). The main
tool for updating probabilities is the logarithmic relative entropy; other
entropies such as those of Renyi or Tsallis are ruled out. We also show that
Bayes updating is a special case of ME updating and thus, that the two are
completely compatible.Comment: Presented at MaxEnt 2006, the 26th International Workshop on Bayesian
Inference and Maximum Entropy Methods (July 8-13, 2006, Paris, France
On the maximum entropy principle and the minimization of the Fisher information in Tsallis statistics
We give a new proof of the theorems on the maximum entropy principle in
Tsallis statistics. That is, we show that the -canonical distribution
attains the maximum value of the Tsallis entropy, subject to the constraint on
the -expectation value and the -Gaussian distribution attains the maximum
value of the Tsallis entropy, subject to the constraint on the -variance, as
applications of the nonnegativity of the Tsallis relative entropy, without
using the Lagrange multipliers method. In addition, we define a -Fisher
information and then prove a -Cram\'er-Rao inequality that the -Gaussian
distribution with special -variances attains the minimum value of the
-Fisher information
Discontinuities in the Maximum-Entropy Inference
We revisit the maximum-entropy inference of the state of a finite-level
quantum system under linear constraints. The constraints are specified by the
expected values of a set of fixed observables. We point out the existence of
discontinuities in this inference method. This is a pure quantum phenomenon
since the maximum-entropy inference is continuous for mutually commuting
observables. The question arises why some sets of observables are distinguished
by a discontinuity in an inference method which is still discussed as a
universal inference method. In this paper we make an example of a discontinuity
and we explain a characterization of the discontinuities in terms of the
openness of the (restricted) linear map that assigns expected values to states.Comment: 8 pages, 3 figures, 32nd International Workshop on Bayesian Inference
and Maximum Entropy Methods in Science and Engineering, Garching, Germany,
15-20 July 201
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