Revisions of the Phenomenological and Statistical Statements of the Second Law of Thermodynamics

The status of the second law of thermodynamics, even in the 21st century, is not as certain as Arthur Eddington wrote about it a hundred years ago. However, it is not about the truth of this principle, but rather about its strict and exhaustive formulation. In the previous article it was shown that two of the three most famous thermodynamic formulations of the second law are non-exhaustive. However, the status of the statistical approach, contrary to common and unfounded opinions, is even more difficult. Well, it is known that Boltzmann did not manage to fully derive the second law from statistical mechanics, even though he did probably everything possible in this regard. In particular, he introduced deterministic chaos into the Liouville equation, obtaining the Boltzmann equation. Using the H theorem, Boltzmann transferred the second law thesis to the molecular chaos hypothesis, which is not considered to be fully true. Therefore, the authors presented a detailed and critical review of the issue of the second law of thermodynamics and entropy from the perspective of phenomenological thermodynamics and statistical mechanics. On this basis, Propositions 1–3 for the second law of thermodynamics were formulated in the original part of the article. It has been proven that Propositions 1–2 in thermodynamic terms are equivalent to the full entropic formulation of the second law. And the probabilistic approach to Proposition 3 was delivered directly. It has been argued that Proposition 3 is in some sense free from Loschmidt’s irreversibility paradox.