# Application of the maximum relative entropy method to the physics of ferromagnetic materials

@article{Giffin2016ApplicationOT, title={Application of the maximum relative entropy method to the physics of ferromagnetic materials}, author={Adom Giffin and Carlo Cafaro and Sean A. Ali}, journal={Physica A-statistical Mechanics and Its Applications}, year={2016}, volume={455}, pages={11-26} }

It is known that the Maximum relative Entropy (MrE) method can be used to both update and approximate probability distributions functions in statistical inference problems. In this manuscript, we apply the MrE method to infer magnetic properties of ferromagnetic materials. In addition to comparing our approach to more traditional methodologies based upon the Ising model and Mean Field Theory, we also test the effectiveness of the MrE method on conventionally unexplored ferromagnetic materials…

## 15 Citations

An information and field theoretic approach to the grand canonical ensemble

- Mathematics, Physics
- 2017

We present a novel derivation of the constraints required to obtain the underlying principles of statistical mechanics using a maximum entropy framework. We derive the mean value constraints by use…

MEMe: An Accurate Maximum Entropy Method for Efficient Approximations in Large-Scale Machine Learning

- Medicine, Computer ScienceEntropy
- 2019

A novel, robust maximum entropy algorithm, which is capable of dealing with hundreds of moments and allows for computationally efficient approximations, is proposed and its usefulness, equivalence to constrained Bayesian variational inference and superiority over existing approaches in two applications are demonstrated.

M ar 2 01 7 An information and field theoretic approach to the grand canonical ensemble

- 2018

We present a novel derivation of the constraints required to obtain the underlying principles of statistical mechanics using a maximum entropy framework. We derive the mean value constraints by use…

Maximum caliber inference and the stochastic Ising model.

- Mathematics, MedicinePhysical review. E
- 2016

This work investigates the maximum caliber variational principle as an inference algorithm used to predict dynamical properties of complex nonequilibrium, stationary, statistical systems in the presence of incomplete information and finds that a convenient choice of the dynamical information constraint together with a perturbative asymptotic expansion with respect to its corresponding Lagrange multiplier leads to a formal overlap with well-known Glauber hyperbolic tangent rule.

Entropic determinants of massive matrices

- Computer Science, Mathematics2017 IEEE International Conference on Big Data (Big Data)
- 2017

The optimality of Maximum Entropy methods in approximating log determinant calculations is demonstrated, it is proved the equivalence between mean value constraints and sample expectations in the big data limit, that Covariance matrix eigenvalue distributions can be completely defined by moment information and that the reduction of the self entropy of a maximum entropy proposal distribution is reduced.

An Information Geometric Perspective on the Complexity of Macroscopic Predictions Arising from Incomplete Information

- Computer Science, PhysicsAdvances in Mathematical Physics
- 2018

This manuscript discusses several illustrative examples wherein the IGAC modeling scheme is employed to infer macroscopic predictions when only partial knowledge of the microscopic nature of a given system is available.

Theoretical investigations of an information geometric approach to complexity

- Computer Science, Physics
- 2017

This article provides several illustrative examples wherein the modeling scheme is used to infer macroscopic predictions when only partial knowledge of the microscopic nature of a given system is available and limitations, possible improvements, and future investigations are discussed.

Reliability Evaluation of Low-voltage Switchgear Based on Maximum Entropy Principle

- Mathematics
- 2017

In this paper, based on the definition of two-parameter joint entropy and the maximum entropy principle, a method was proposed to determine the prior distribution by using the maximum entropy method…

Information geometric complexity of entropic motion on curved statistical manifolds under different metrizations of probability spaces

- Mathematics, PhysicsInternational Journal of Geometric Methods in Modern Physics
- 2019

We investigate the effect of different metrizations of probability spaces on the information geometric complexity of entropic motion on curved statistical manifolds. Specifically, we provide a…

Entropic Trace Estimates for Log Determinants

- Mathematics, Computer ScienceECML/PKDD
- 2017

This work estimates log determinants under the framework of maximum entropy, given information in the form of moment constraints from stochastic trace estimation, demonstrating a significant improvement on state-of-the-art alternative methods.

## References

SHOWING 1-10 OF 45 REFERENCES

Using Relative Entropy to Find Optimal Approximations: an Application to Simple Fluids

- Mathematics, PhysicsArXiv
- 2008

The central results consist of justifying the use of relative entropy as the uniquely natural criterion to select a preferred approximation from within a family of trial parameterized distributions, and to obtain the optimal approximation by marginalizing over parameters using the method of maximum entropy and information geometry.

Information Theory and Statistical Mechanics

- Mathematics
- 1957

Treatment of the predictive aspect of statistical mechanics as a form of statistical inference is extended to the density-matrix formalism and applied to a discussion of the relation between…

Some generalized order - disorder transformations

- Physics
- 1952

In considering the statistics of the ‘no-field’ square Ising lattice in which each unit is capable of two configurations and only nearest neighbours interact, Kramers and Wannier (3) were able to…

Information Geometry, Inference Methods and Chaotic Energy Levels Statistics

- Physics, Mathematics
- 2008

In this Letter, we propose a novel information-geometric characterization of chaotic (integrable) energy level statistics of a quantum antiferromagnetic Ising spin chain in a tilted (transverse)…

Can chaotic quantum energy levels statistics be characterized using information geometry and inference methods

- Mathematics, Physics
- 2008

In this paper, we review our novel information-geometrodynamical approach to chaos (IGAC) on curved statistical manifolds and we emphasize the usefulness of our information-geometrodynamical entropy…

Variational Principle of Bogoliubov and Generalized Mean Fields in Many-Particle Interacting Systems

- Physics, Mathematics
- 2015

The approach to the theory of many-particle interacting systems from a unified standpoint, based on the variational principle for free energy is reviewed. A systematic discussion is given of the…

Updating Probabilities with Data and Moments

- Physics, Computer ScienceArXiv
- 2007

The generic “canonical” form of the posterior distribution for the problem of simultaneous updating with data and moments is obtained and the general problem of non‐commuting constraints, when they should be processed sequentially and when simultaneously is discussed.

Two-Dimensional Ising Model as a Soluble Problem of Many Fermions

- Physics
- 1964

The two-dimensional Ising model for a system of interacting spins (or for the ordering of an AB alloy) on a square lattice is one of the very few nontrivial many-body problems that is exactly soluble…

Fundamentals of Statistical and Thermal Physics

- Materials Science
- 1965

This book is designed for the junior-senior thermodynamics course given in all departments as a standard part of the curriculum. The book is devoted to a discussion of some of the basic physical…

From Physics to Economics: An Econometric Example Using Maximum Relative Entropy

- Mathematics, Computer ScienceArXiv
- 2009

It is demonstrated how information in the form of observable data and moment constraints are introduced into the method of Maximum relative Entropy (MrE), which can be used as templates for real world problems.