The Assumptions in Boltzmann's Minimum Theorem

Abstract

MR. CULVERWELL'S letter in your issue of April 18 leaves many important points in connection with the reversibility of Boltzmann's Minimum Theorem untouched. On the question as to what different people mean (or think they mean) when they assert that the theorem is true, enough has already been said. What we want to know is what assumptions are involved in the mathematical proofs of the theorem, why they have to be made, and for what systems they are likely to hold. This question has been ably treated by Mr. Burbury, but in view of Prof. Boltzmann's assertion that the theorem is one of probability, it is desirable to examine more fully where probability considerations enter into proofs such as Dr. Watson's, which contain no explicit reference to them.