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Related papers: The maximum relative entropy principle

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Borrowing the idea of topological pressure determining measure-theoretical entropy in topological dynamical systems, we establish a variational principle for upper metric mean dimension with potential in terms of upper measure-theoretical…

Dynamical Systems · Mathematics 2024-12-30 Rui Yang , Ercai Chen , Xiaoyao Zhou

I show that the maximum entropy principle can be replaced by a more natural assumption, that there exists a phenomenological function of entropy consistent with the microscopic model. The requirement of existence provides then a unique…

Classical Physics · Physics 2014-07-22 Łukasz Rudnicki

Entropy plays a key role in statistical physics of complex systems, which in general exhibit diverse aspects of emergence on different scales. However, it still remains not fully resolved how entropy varies with the coarse-graining level…

Statistical Mechanics · Physics 2017-08-07 Segun Goh , Jungzae Choi , MooYoung Choi , Byung-Gook Yoon

High-order phenomena play crucial roles in many systems of interest, but their analysis is often highly nontrivial. There is a rich literature providing a number of alternative information-theoretic quantities capturing high-order…

Information Theory · Computer Science 2024-10-15 Fernando E. Rosas , Aaron Gutknecht , Pedro A. M. Mediano , Michael Gastpar

Maximum entropy models provide the least constrained probability distributions that reproduce statistical properties of experimental datasets. In this work we characterize the learning dynamics that maximizes the log-likelihood in the case…

Disordered Systems and Neural Networks · Physics 2016-09-21 Ulisse Ferrari

Econophysics, is based on the premise that some ideas and methods from physics can be applied to economic situations. We intend to show in this paper how a physics concept such as entropy can be applied to an economic problem. In so doing,…

Statistical Finance · Quantitative Finance 2016-09-08 Adom Giffin

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

The purpose of this paper is to generalize the variational principle, which states that the topological entropy is equal to the supremum of the measure theoretical entropies and also the minimum of the metric theoretical entropies, to…

Dynamical Systems · Mathematics 2013-12-04 Zheng Wei , Yangeng Wang , Guo Wei , Zhiming Li , Tonghui Wang

This paper modifies Jaynes's axioms of plausible reasoning and derives the minimum relative entropy principle, Bayes's rule, as well as maximum likelihood from first principles. The new axioms, which I call the Optimum Information…

Information Theory · Computer Science 2011-03-30 Alexis Akira Toda

A generic feature of systems with long-range interactions is the presence of {\it quasi-stationary} states with non-Gaussian single particle velocity distributions. For the case of the Hamiltonian Mean Field (HMF) model, we demonstrate that…

The maximum entropy principle advocates to evaluate events' probabilities using a distribution that maximizes entropy among those that satisfy certain expectations' constraints. Such principle can be generalized for arbitrary decision…

Machine Learning · Statistics 2021-12-16 Santiago Mazuelas , Yuan Shen , Aritz Pérez

We show that the Jaynes principle is indeed a proper inference scheme when applied to compound systems and will correctly produce the entangled maximum entropy states compatible with appropriate data. This is accomplished by including the…

Quantum Physics · Physics 2008-12-18 A. K. Rajagopal

The quantum relative entropy is a fundamental quantity in quantum information science, characterizing the distinguishability between two quantum states. However, this quantity is not additive in general for correlated quantum states,…

Quantum Physics · Physics 2025-06-05 Kun Fang , Hamza Fawzi , Omar Fawzi

We investigate the detailed properties of Observational entropy, introduced by \v{S}afr\'{a}nek et al. [Phys. Rev. A 99, 010101 (2019)] as a generalization of Boltzmann entropy to quantum mechanics. This quantity can involve multiple…

Quantum Physics · Physics 2019-01-17 Dominik Šafránek , J. M. Deutsch , Anthony Aguirre

In an essential and quite general setup, based on networks, we identify Schnakenberg's observables as the constraints that prevent a system from relaxing to equilibrium, showing that, in the linear regime, steady states satisfy a minimum…

Statistical Mechanics · Physics 2015-05-28 Matteo Polettini

Our everyday descriptions of the universe are highly coarse-grained, following only a tiny fraction of the variables necessary for a perfectly fine-grained description. Coarse graining in classical physics is made natural by our limited…

Quantum Physics · Physics 2008-11-26 Murray Gell-Mann , James Hartle

We investigate the effect of coarse-graining on the energetics properties of a system, focusing on entropy production. As a case of study, we consider a one-dimensional colloidal particle in contact with a thermal bath, moving in a…

Statistical Mechanics · Physics 2021-09-08 Pierpaolo Bilotto , Lorenzo Caprini , Angelo Vulpiani

Entropy is a central concept in physics, but can be challenging to calculate even for systems that are easily simulated. This is exacerbated out of equilibrium, where generally little is known about the distribution characterizing simulated…

Statistical Mechanics · Physics 2024-05-09 Samuel D. Gelman , Guy Cohen

The variational method is very important in mathematical and theoretical physics because it allows us to describe the natural systems by physical quantities independently from the frame of reference used. A global and statistical approach…

Mathematical Physics · Physics 2011-01-10 Umberto Lucia

Quantum mechanics is derived as an application of the method of maximum entropy. No appeal is made to any underlying classical action principle whether deterministic or stochastic. Instead, the basic assumption is that in addition to the…

Quantum Physics · Physics 2011-05-09 Ariel Caticha