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We will discuss the maximum entropy production (MaxEP) principle based on Jaynes' information theoretical arguments, as was done by Dewar (2003, 2005). With the help of a simple mathematical model of a non-equilibrium system, we will show…

Statistical Mechanics · Physics 2009-11-13 Stijn Bruers

It is by now well known that the Boltzmann-Gibbs-von Neumann-Shannon logarithmic entropic functional ($S_{BG}$) is inadequate for wide classes of strongly correlated systems: see for instance the 2001 Brukner and Zeilinger's {\it Conceptual…

Statistical Mechanics · Physics 2015-05-20 Constantino Tsallis

This paper mainly focuses on studying the Shannon Entropy and Kullback-Leibler divergence of the multivariate log canonical fundamental skew-normal (LCFUSN) and canonical fundamental skew-normal (CFUSN) families of distributions, extending…

Statistics Theory · Mathematics 2016-09-21 Marina Muniz , Roger Silva , Rosangela Loschi

We study maximum-entropy inference for finite-dimensional quantum states under linear moment constraints. Given expectation values of finitely many observables, the feasible set of states is convex but typically non-unique. The…

Quantum Physics · Physics 2025-10-27 James Tian

We present a new class of estimators of Shannon entropy for severely undersampled discrete distributions. It is based on a generalization of an estimator proposed by T. Schuermann, which itself is a generalization of an estimator proposed…

Information Theory · Computer Science 2021-11-30 Peter Grassberger

We present a general holistic theory for the organization of complex networks, both human-engineered and naturally-evolved. Introducing concepts of value of interactions and satisfaction as generic network performance measures, we show that…

Adaptation and Self-Organizing Systems · Physics 2007-07-13 Venkat Venkatasubramanian , Dimitris N. Politis , Priyan R. Patkar

Concept of exponential family is generalized by simple and general exponential form. Simple and general potential are introduced. Maximum Entropy and Maximum Likelihood tasks are defined. ML task on the simple exponential form and ME task…

Statistics Theory · Mathematics 2019-08-17 Marian Grendar, , Marian Grendar

We present a technique for entropy optimization to calculate a distribution from its moments. The technique is based upon maximizing a discretized form of the Shannon entropy functional by mapping the problem onto a dual space where an…

Disordered Systems and Neural Networks · Physics 2009-11-10 K. Bandyopadhyay , A. K. Bhattacharya , Parthapratim Biswas , D. A. Drabold

It is shown that the standard expression for the information entropy, originally due to Shannon, is only valid for a particular set of states. For the general case of statistical mechanics, one needs to include an additional term in the…

Statistical Mechanics · Physics 2012-09-26 Phil Attard

We shall prove that the celebrated R\'enyi entropy is the first example of a new family of infinitely many multi-parametric entropies. We shall call them the $Z$-entropies. Each of them, under suitable hypotheses, generalizes the celebrated…

Mathematical Physics · Physics 2017-02-07 Piergiulio Tempesta

We explore a recently introduced quantum thermodynamic entropy $S^Q_{univ}$ of a pure state of a composite system-environment computational "universe" with a simple system $\mathcal{S}$ coupled to a constant temperature bath $\mathcal{E}$.…

Quantum Physics · Physics 2022-11-28 Phillip C. Lotshaw , Michael E. Kellman

We show that the naive application of the maximum entropy principle can yield answers which depend on the level of description, i.e. the result is not invariant under coarse-graining. We demonstrate that the correct approach, even for…

Statistical Mechanics · Physics 2007-05-23 Jayanth Banavar , Amos Maritan

Systems with long-range interactions display a short-time relaxation towards Quasi Stationary States (QSS) whose lifetime increases with the system size. In the paradigmatic Hamiltonian Mean-field Model (HMF) out-of-equilibrium phase…

Statistical Mechanics · Physics 2016-02-15 Gabriele Martelloni , Gianluca Martelloni , Pierre de Buyl , Duccio Fanelli

Statistical physics aims to describe properties of macroscale systems in terms of distributions of their microscale agents. Its central tool is the maximization of entropy, a variational principle. We review the history of this principle,…

Statistical Mechanics · Physics 2023-10-11 Jonathan Asher Pachter , Ying-Jen Yang , Ken A. Dill

We propose a compression-based version of the empirical entropy of a finite string over a finite alphabet. Whereas previously one considers the naked entropy of (possibly higher order) Markov processes, we consider the sum of the…

Information Theory · Computer Science 2011-04-05 Paul M. B. Vitányi

In many applications, the probability density function is subject to experimental errors. In this work the continuos dependence of a class of generalized entropies on the experimental errors is studied. This class includes the C. Shannon,…

Data Analysis, Statistics and Probability · Physics 2016-05-20 György Steinbrecher , Giorgio Sonnino

The maximum-entropy sampling problem (MESP) aims to select the most informative principal submatrix of a prespecified size from a given covariance matrix. This paper proposes an augmented factorization bound for MESP based on concave…

Optimization and Control · Mathematics 2024-10-15 Yongchun Li

We consider the Shannon-Khinchin axiomatic systems for the characterization of generalized entropies such as Sharma-Mital and Frank-Daffertshofer entropy. We provide the generalization of Shannon-Khinchin axioms and give the corresponding…

Mathematical Physics · Physics 2015-06-17 Velimir M. Ilic , Miomir S. Stankovic

Moment-closure methods are popular tools to simplify the mathematical analysis of stochastic models defined on networks, in which high dimensional joint distributions are approximated (often by some heuristic argument) as functions of lower…

Data Analysis, Statistics and Probability · Physics 2011-05-25 Tim Rogers

This paper investigates a function of macroscopic variables known as the singular potential, building on previous work by Ball and Majumdar. The singular potential is a function of the admissible statistical averages of probability…

Analysis of PDEs · Mathematics 2016-07-18 Jamie M. Taylor