TY - JOUR
T1 - On the application of statistical mechanics to the general dynamics of matter and ether
JF - Proceedings of the Royal Society of London. Series A
JO - Proc R Soc Lond A Math Phys Sci
SP - 296
LP - 311
M3 - 10.1098/rspa.1905.0029
VL - 76
IS - 510
AU -
Y1 - 1905/07/10
UR - http://rspa.royalsocietypublishing.org/content/76/510/296.abstract
N2 - 1. One branch of abstract dynamics, which is, perhaps, best known under the name of Statistical Mechanics, attempts to discover as much as possible about the motion of a dynamical system when the specification of the system is either partially or fully known, but the initial configuration of the system is either not known at all, or is only partially known. A complete solution of the problem would require not only a full knowledge of the dynamical specification of the system, but also a full knowledge of the initial configuration of the system. These not being given, it is obvious that the problem cannot be fully solved. The method of statistical mechanics is as follows: We divide up all possible configurations of the system into mutually exclusive classes, A1, A2, A3,...An, and calculate the corresponding classes of solution after time t corresponding to the initial configurations of classes A1, A2... . Let us call the final classes of solutions B1, B2, B3... . In selecting the original classes A1, A2..., we arrange that the values of any co-ordinate in any class A shall differ so slightly from one another that the final values of the same co-ordinate in the solution B shall also only differ slightly from one another. The calculation proceeds by an appeal to the calculus of probabilities. Let p1, p2,. . . pn be the unknown probabilities that the co-ordinates of the initial system belong to the classes A1, A2,. . . .An, so that p1 + p2+. . .pn = 1.
ER -