On various functions called entropy when using classical mechanics

Thermodynamic entropy and four different functions used to describe it within mechanical models are considered. It is shown that all four variants have properties that differ significantly from the properties of entropy introduced in thermodynamics based on experimental data. It is established that, in order to comply with the approaches used in thermodynamics, the widely used mechanical model of a rarefied gas should consider almost exclusively processes that assume the presence of external forces acting on the system. It is noted that such a requirement allows a new approach to the use of mechanical models for studying irreversible physical phenomena.