Letter | Published:

On the Minimum Theorem in the Theory of Gases

Nature volume 52, page 221 | Download Citation

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Abstract

You would oblige me by inserting the following lines in NATURE. The last remark made by Mr. Burbury points out, indeed, the weakest point of the demonstration of the H-theorem. If condition (A) is fulfilled at t = O, it is not a mechanical necessity that it should be fulfilled at all subsequent times. But let the mean path of a molecule be very long in comparison with the average distance of two neighbouring molecules; then the absolute position in space of the place where one impact of a given molecule occurs, will be far removed from the place where the next impact of the same molecule occurs. For this reason, the distribution of the molecules surrounding the place of the second impact will be independent of the conditions in the neighbourhood of the place where the first impact occurred, and therefore independent of the motion of the molecule itself. Then the probability that a second molecule moving with given velocity should fall within the space traversed by the first molecule, can be found by multiplying the volume of this space by the function f. This is condition (A).

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  1. 9 Tuerkenstrasse, Vienna, June 20.

    • LUDWIG BOLTZMANN

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DOI

https://doi.org/10.1038/052221b0

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