no BELL SYSTEM TECHNICAL JOURNAL 



anics is the science which professes that, given the positions and momenta 

 and the forces in a system of particles at 10 A.M. sharp, it can predict the 

 positions and momenta of all the particles at 11 A.M. and every instant in 

 between and all through the endless future. Statistical mechanics, for all 

 the implications of its name, is nowhere nearly so audacious. 



Suppose the electric fan, or whatever stirring-gadget was employed, was 

 stopped an instant before 10 A.M. sharp. S.M. hmits itself to affirming 

 that at 11 A.M. the most probable state for the gas in the container — the 

 immensely most probable state, the almost-certain state — is the uniform 

 state. It also says the same thing exactly for 10:15 A.M., and for 10:01 

 A.M., and even for 10 A.M. sharp. If at 10 A.M. sharp the gas is in a state 

 of wild and furious surging, S.M. does not deny the fact, but sees no reason 

 for revising its own affirmation. If at 10:01 A.M. the gas is settling down 

 but has not yet quite reached the uniform state, that again does not deter 

 S.M. from standing by its assertion. Whenever a freak of chance or act of 

 man may have produced one of the states which it calls improbable, S.M. 

 just says "wait, and you shall have the state which / am going to talk about." 

 To further questions it can only say "I know my limits" — and that is what 

 its basic theorem says for it. 



If now the negative aspect of the basic theorem is sufficiently clear, we may 

 address ourselves to the task of giving the theorem a positive meaning. For 

 this there is but one way: the word "probability" must be replaced with 

 some word or phrase or mathematical expression which does have a meaning. 

 After this is done we can of course restore the word "probability" as an 

 equivalent for that other word or expression. The basic theorem will then 

 be tautological upon the surface only, for actually it will have the meaning 

 conferred upon it by the deiinition of its key-word. 



Various meanings have been offered for the key-word, by various people 

 who have been successful in getting useful results out of statistical mechanics. 

 Until 1924 the dominant meaning was that imposed by Gibbs and Boltz- 

 mann. From this meaning arises the form of S.M. which is called "the classi- 

 cal statistics". (The word "statistics", by the way, is a bad but common 

 abbreviation for "statistical mechanics".) This is the topic of the present 

 article. In 1924 there was proposed a novel meaning for the key-word, 

 which led to results sometimes agreeing with, sometimes differing from, those 

 attained by the classical statistics. W'here the results of the two agreed, 

 they agreed with experiment also; where the results of the two disagreed, 

 experiment sustained the new one. This event has left the classical statis- 

 tics in a strange situation, in which one cannot exclude the possibility that 

 all of its remarkable achievement is due to a happy but deceptive chance. 

 The classical statistics may indeed be only a past episode in the history of 

 scientific thought, and it is for this reason that I have given to the article the 



