show that in the fully dimerized limit the GIMs should all have the same magnitude, and that the sign of odd GIMs switch sign with respect to the direction of the polarization. We also focus on the line of the parameter plane where the polarization shows a line of discontinuity (see Fig. \[fig:mom1\], lower panel, left inset). We also present two model calculations in which the evolution of the probability distribution is followed around the topologically nontrivial point of the RM model. As expected, the distribution migrates to the next unit cell, although its shape varies considerably during the cycle.

Reconstructing a probability distribution from knowledge of a finite set of moments is an ill-posed mathematical problem which already has a long history [@Smoluchowski17], although there has been a renewed interest in the last decades [@John07; @DeSouza10]. The scientific applications are also quite broad; image processing [@Sluzek05], calculating magnetic moments [@Berkov00], or molecular electronic structure [@Bandyopadhyay05]. In our study, we opt for a reconstruction based on maximizing the entropy [@Bandyopadhyay05; @Collins77; @Mead84] of the underlying probability distribution.

This paper is organized as follows. In the next section we introduce the GICs associated with the Zak phase. We then discuss their 