Was Loschmidt Correct in Asserting that the Entropy of a Closed System can be Decreased?

The laws of thermodynamics are a set of scientific principles that define a set of physical properties that describe thermodynamic systems in thermodynamic equilibrium, including temperature, energy, and entropy. J.C. Maxwell demonstrated in 1868 that if the equilibrium temperature in a vertical column of gas subject to gravity was a function of height, a perpetual motion machine of the second sort would be achievable. Maxwell, on the other hand, maintained that the temperature must be the same at all locations down the column. Boltzmann felt the same way. Loschmidt was their opponent. He asserted that the equilibrium temperature decreased with height and that a perpetual motion machine of the second sort running through such a column was compatible with his interpretation of the second law of thermodynamics. As a result, he was confident he had discovered an infinite supply of useful energy for humanity. Later, E. Mach, too, did not consider the development of a second-generation perpetual motion machine to be impossible, although he did not cite Loschmidt's notion. In this article, new arguments (based on statistical mechanics) are provided for the hypothesis that an insulated column of gas subject to gravity does not take on a homogenous temperature: Since Boltzmann’s distribution of energies leads to the general gas law even in case the molecules are supposed to be extended objects, it follows that Boltzmann’s distribution cannot be strictly valid if experience requires to replace the general gas law pV=NkT by p(V-b) = NkT. But such a modification of the general gas law is undoubtedly required. With a modification of the general gas law and hence a deviation from Boltzmann’s distribution of energies thus being indispensable, it further follows that a homogeneous temperature cannot be achieved in an insulated column if gas subject to gravity.