LANGEVIN, PAUL.

Sur la théorie du mouvement brownien.

(Paris: Gauthier-Villars), 1908. 4to. No wrappers. In: "Comptes Rendus Hebdomadaires des Seances de l'Academie des Sciences", Vol 146, No 10. Entire issue offered. Pp. 530-33. [Entire issue: Pp. 511-54].

First appearance of Langevin landmark paper in which "Langevin successfully applied Newtonian dynamics to a Brownian particle and so invented an analytical approach to random processes which has remained useful to this day." (Lemonsa, Paul Langevin’s 1908 paper, P. 1079).

In 1908, three years after Albert Einstein initiated the modern study of random processes with his ground breaking paper on Brownian motion, Paul Langevin devised a very different but likewise successful description of Brownian motion. Both descriptions have since been generalized
into mathematically distinct but physically equivalent tools for studying an important class of continuous random processes. Langevin's work, like Einstein's, remains current and is widely referenced and discussed.

"Langevin's approach to Brownian motion is, in his own words, ''in?nitely more simple'' than Einstein's. Indeed, his paper is apparently more simple and for this reason is attractive as an introduction to the subject. While Einstein, starting from reasonable hypotheses, derived and solved a partial differential equation (i.e., a Fokker-Planck equation) Governing the time evolution of the probability density of a Brownian particle, Langevin applied Newton's second law to a representative Brownian particle. In this way Langevin invented the ''F=ma'' of stochastic physics now called the ''Langevin equation.'' Today it is clear that the apparent simplicity of Langevin's approach was purchased at the cost of forcing into existence new mathematical objects with unusual properties. While Langevin manipulated these objects (Gaussian white noise and the stochastic differential equation) cautiously and intuitively, their formal properties have now been developed and widely applied. Thus Langevin's 1908 paper inspired new mathematics as well as new physics." (Lemonsa, Paul Langevin’s 1908 paper, P. 1082).

"In 1908, Langevin, whose skill in kinetic theory had first been developed when he worked on ionic transport, turned briefly to the theory of Brownian motion developed by Einstein in 1905 and, via a more direct route, by Smoluchowski in 1906. The result was simplified, still-standard treatment which, unlike Smoluchowski’s, produced precisely Einstein’s formula for the mean-square displacement." (DSB)

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Order-nr.: 48627