Josef Loschmidt

Johan Josef Loschmidt was an assistant to the first Franz Serafin Exner. He read to Exner when the older man's eyesight failed, so was likely quite familiar with Exner's effort to instill probabilistic thinking into the minds of young Austrians.

In 1865, Loschmidt was the first to estimate the size of air molecules. His result was only twice the true size, a remarkable feat given the approximations he had to make. He was able to determine how many molecules are present in a given volume of gas (about 6 x 1023 molecules per gram molecular weight or "mole" of a gas). This is known as the "Loschmidt constant" in Europe, and "Avogadro's number" in England and America. Avogadro had in 1811 proposed the existence of such a number, but Loschmidt actually determined it first.

Loschmidt became the most important mentor of the young Ludwig Boltzmann, and later the first serious critic of Boltzmann's H-Theorem, which Boltzmann derived during the 1860's.

Loschmidt suggested to Boltzmann that the entropy would decrease if the directions of motion of all the molecules were reversed. This is equivalent to assuming that time could be reversed (see the Arrow of Time). The equations of classical dynamics are time reversible, so, in principle, one could reverse the increasing disorder of gas particles, returning the perfume molecules to a bottle that was opened at time t0, for example.

This came to be known as the "Reversibility paradox" or "Loschmidt's paradox."

It is related to a similar attack on Boltzmann's derivation of entropy increase by Ernst Zermelo thirty years later called "Zermelo's paradox or the "Recurrence paradox."

Loschmidt's criticism caused Boltzmann to revise his arguments and claim that there must be a fundamental "molecular disorder" at work that randomizes molecular motions during collisions.

Information physics can show that neither the "Reversibility paradox" nor the "Recurrence paradox" are actual problems.

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