  We analyze multi-point correlation functions of a tracer in an incompressible
flow at scales far exceeding the scale $L$ at which fluctuations are generated
(quasi-equilibrium domain) and compare them with the correlation functions at
scales smaller than $L$ (turbulence domain). We demonstrate that the scale
invariance can be broken in the equilibrium domain and trace this breakdown to
the statistical integrals of motion (zero modes) as has been done before for
turbulence. Employing Kraichnan model of short-correlated velocity we identify
the new type of zero modes, which break scale invariance and determine an
anomalously slow decay of correlations at large scales.
