A cautionary tale of entropic criteria in assessing the validity of the maximum entropy principle

¹ NYUAD Institute, New York University Abu Dhabi - Abu Dhabi, United Arab Emirates
² CAS Key Laboratory of Brain Function and Disease, CAS Center for Excellence in Brain Science and Intelligence Technology, and School of Life Sciences, University of Science and Technology of China - Anhui, China
³ School of Mathematical Sciences, MOE- LSC and Institute of Natural Sciences, Shanghai Jiao Tong University Shanghai, PRC
⁴ Courant Institute of Mathematical Sciences and Center for Neural Science, New York University New York, NY, USA

^(a) zhiqinxu@nyu.edu
^(b) zdz@sjtu.edu.cn

Received: 8 November 2018
Accepted: 16 May 2019

Abstract

The maximum entropy principle (MEP) has been applied to study various problems in equilibrium and nonequilibrium systems in physics and other disciplines. Through analyses of numerical and experimental data, we demonstrate that the widely used entropic criteria, an assessment of the validity of MEP, can be misleading indexes as they can often fail to reflect the important difference between the observed and the MEP predicted statistical distribution. Our work demonstrates the importance of high-order statistical structures that cannot be captured by the entropic criteria and provides a cautionary tale of over-interpretation of results of MEP.

This paper is dedicated to David Cai.