Related papers: Maximum Entropy Principle, Equal Probability a Pri…
(Jaynes') Method of (Shannon-Kullback's) Relative Entropy Maximization (REM or MaxEnt) can be - at least in the discrete case - according to the Maximum Probability Theorem (MPT) viewed as an asymptotic instance of the Maximum Probability…
We generalize the usual exponential Boltzmann factor to any reasonable and potentially observable distribution function, $B(E)$. By defining generalized logarithms $\Lambda$ as inverses of these distribution functions, we are led to a…
The Gibbs entropy of a macroscopic classical system is a function of a probability distribution over phase space, i.e., of an ensemble. In contrast, the Boltzmann entropy is a function on phase space, and is thus defined for an individual…
Given physical systems, counting rule for their statistical mechanical descriptions need not be unique, in general. It is shown that this nonuniqueness leads to the existence of various canonical ensemble theories which equally arise from…
We derive the microcanonical ensemble from the Maximum Entropy Principle (MEP) using the phase space volume entropy of P. Hertz. Maximizing this entropy with respect to the probability distribution with the constraints of normalization and…
The main goal of this paper is to extend and apply the principle of maximum entropy (MaxEnt) to incomplete quantum process estimation tasks. We will define a so-called process entropy function being the von Neumann entropy of the state…
The Boltzmann-Wallis-Jaynes' multiplicity argument is taken up and elaborated. MaxEnt is proved and demonstrated to be just an asymptotic case of looking for such a vector of absolute frequencies in a feasible set, which has maximal…
A common statistical situation concerns inferring an unknown distribution Q(x) from a known distribution P(y), where X (dimension n), and Y (dimension m) have a known functional relationship. Most commonly, n<m, and the task is relatively…
The kinematics and dynamics of deterministic physical systems have been a foundation of our understanding of the world since Galileo and Newton. For real systems, however, uncertainty is largely present via external forces such as friction…
We discuss how the method of maximum entropy, MaxEnt, can be extended beyond its original scope, as a rule to assign a probability distribution, to a full-fledged method for inductive inference. The main concept is the (relative) entropy…
We study the maximum entropy (MaxEnt) approach for analytical continuation of spectral data from imaginary times to real frequencies. The total error is divided in a statistical error, due to the noise in the input data, and a systematic…
The maximum entropy principle (MEP) is a method for obtaining the most likely distribution functions of observables from statistical systems, by maximizing entropy under constraints. The MEP has found hundreds of applications in ergodic and…
MaxEnt's variational principle, in conjunction with Shannon's logarithmic information measure, yields only exponential functional forms in straightforward fashion. In this communication we show how to overcome this limitation via the…
Maximum entropy (Maxent) models are a class of statistical models that use the maximum entropy principle to estimate probability distributions from data. Due to the size of modern data sets, Maxent models need efficient optimization…
In density estimation task, maximum entropy model (Maxent) can effectively use reliable prior information via certain constraints, i.e., linear constraints without empirical parameters. However, reliable prior information is often…
Using the Dissipation Theorem and a corollary of the Fluctuation Theorem, namely the Second Law Inequality, we give a first-principles derivation of Boltzmann's postulate of equal a priori probability in phase space for the microcanonical…
Introduced by Boltzmann under the name "monode," the microcanonical ensemble serves as the fundamental representation of equilibrium thermodynamics in statistical mechanics by counting all possible realizations of a system's states.…
This paper is a review of a particular approach to the method of maximum entropy as a general framework for inference. The discussion emphasizes the pragmatic elements in the derivation. An epistemic notion of information is defined in…
Recent work in data mining and related areas has highlighted the importance of the statistical assessment of data mining results. Crucial to this endeavour is the choice of a non-trivial null model for the data, to which the found patterns…
Inferring a quantum system from incomplete information is a common problem in many aspects of quantum information science and applications, where the principle of maximum entropy (MaxEnt) plays an important role. The quantum state…