Shadowability of statistical averages in chaotic systems

Abstract

An important problem in statistical and nonlinear physics is whether the statistical averages can be computed or measured reliably. In particular, a relevant situation is where measurements of average physical quantities take place. The findings imply that if an identical experiment is to be performed in two different environments or at two different times where the noise levels are different, the measured averages of some physical quantities may vary. Since computing or measuring averages is an extremely common practice in physics and in many other scientific disciplines as well, such a finding may be of fundamental importance.