Information geometry, simulation and complexity in Gaussian random fields

Author:

Levada Alexandre L.

Abstract

AbstractRandom fields are useful mathematical objects in the characterization of non-deterministic complex systems. A fundamental issue in the evolution of dynamical systems is how intrinsic properties of such structures change in time. In this paper, we propose to quantify how changes in the spatial dependence structure affect the Riemannian metric tensor that equips the model's parametric space. Defining Fisher curves, we measure the variations in each component of the metric tensor when visiting different entropic states of the system. Simulations show that the geometric deformations induced by the metric tensor in case of a decrease in the inverse temperature are not reversible for an increase of the same amount, provided there is significant variation in the system's entropy: the process of taking a system from a lower entropy state A to a higher entropy state B and then bringing it back to A, induces a natural intrinsic one-way direction of evolution. In this context, Fisher curves resemble mathematical models of hysteresis in which the natural orientation is pointed by an arrow of time.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,Statistics and Probability

Reference41 articles.

1. Information theory and statistical mechanics Information theory and statistical mechanicsPhys;Jaynes;Phys Rev Rev,1957

2. Markov random fields and Gibbs ensembles Markov random fields and Gibbs ensemblesAmer Monthly;Spitzer;Amer Math Monthly Math,1971

3. Crystal statistics A two - dimensional model with an order - disorder transition Crystal statistics A two - dimensional model with an order - disorder transitionPhys;Onsager;Phys Rev Rev,1944

4. Information geometry on hierarchy of probability distributions Information geometry on hierarchy of probability distributionsIEEE Trans Theory;Amari;IEEE Trans Inform Theory Inform,2001

5. Exploring e - science : An introduction Computer Mediated Commun Exploring e - science : An introductionJ Computer Mediated;Jankowski;Commun,2007

Cited by 4 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3