Conservation Laws in Thermodynamics and Statistical Physics

Analysis of the application for conservation laws of mass, momentum and energy in the description of thermodynamic and statistical processes is performed. The fundamental limitations of the energy conservation law, which is traditionally used in phenomenological thermodynamics, are demonstrated. The correspondence of Hamilton's statistical equations and the phenomenological conservation laws of momentum and energy is considered. The procedure for obtaining and properties of the Liouville phase volume conservation law in statistical physics is analyzed. The presented analysis reveals a deep unity of phenomenological and statistical approaches to the study of our nature.