Solution

I consider this problem to be a cornerstone of this section. In my opinion, it is this specific problem that fully reveals the probabilistic thermodynamic approach in statistical physics. Some might find the solution overly detailed, but I would like to demonstrate it in the style of Sivukhin's methodology. Any macrostate of a system characterized by pressure, volume, and temperature is realized by a vast number of microstates—that is, by a specific set of coordinates and momenta of all molecules. The number of such microstates represents the thermodynamic probability $W$. According to the second law of thermodynamics, an isolated system can spontaneously transition only from a less probable state to a more probable one. That is, for any real process, the ratio of the final probability of the system to the initial one must be: