Generalization of the Bogoliubov–Zubarev theorem for dynamic pressure to the case of compressibility

We present the motivation, formulation, and modified proof of the Bogoliubov–Zubarev theorem connecting the pressure of a dynamical object with its energy within the framework of a classical description and obtain a generalization of this theorem to the case of dynamical compressibility. In both cases, we introduce the volume of the object into consideration using a singular addition to the Hamiltonian function of the physical object, which allows using the concept of the Bogoliubov quasiaverage explicitly already on a dynamical level of description. We also discuss the relation to the same result known as the Hellmann–Feynman theorem in the framework of the quantum description of a physical object.