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

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.