In condensed matter physics, simplified descriptions are obtained by coarse-graining the features of a system at a certain characteristic length, defined as the typical length beyond which some properties are no longer correlated. From a physics standpoint, in vitro DNA has thus a characteristic length of 300 base pairs (bp), the Kuhn length of the molecule beyond which correlations in its orientations are typically lost. From a biology standpoint, in vivo DNA has a characteristic length of 1000 bp, the typical length of genes. Since bacteria live in very different physico-chemical conditions and since their genomes lack translational invariance, whether larger, universal characteristic lengths exist is a non-trivial question. In this talk, I will present an analysis of GC content correlations and of the evolutionary conservation of gene contexts (synteny) in hundreds of bacterial chromosomes, which reveals the existence of a fundamental characteristic length around 10-20 kb. This characteristic length reflects elementary structures involved in the coordination of gene expression, which are present all along the genome of nearly all bacteria.