Phase space of collective variables and the Zubarev transition function

We study the completeness of the transition function $J(\rho-\hat\rho)$ to the infinite set of collective variables $\{\rho_{\mathbf k}\}$. Zubarev first introduced this transition function in statistical physics. We propose complete forms for the Jacobians of transitions to the corresponding sets of collective variables in problems in the theory of electrolyte solutions, the Ising model, and the first-order phase transition. We analyze the methods and calculation results in the phase spaces of collective variables of the partition functions of these systems.