A history of the relation between fluctuation and dissipation

Abstract

A first relation between fluctuation and dissipation occurred in 1905–1908 in the theories of Brownian motion by Albert Einstein, Marian Smoluchowki, and Paul Langevin. Another famous occurrence is in Harry Nyquist's theory of thermal noise in resistors (1927). Many physicists are also aware of the general results and theorems later obtained by Lars Onsager, Herbert Callen, and Ryogo Kubo through highly ingenious reasoning. Also important though mostly forgotten were the direct or indirect contributions by Walther Nernst, John Kirkwood, Melville Green, and Hidetosi Takahasi. Little is known on the context and genesis of these multiple achievements. In this historical study, they will be traced partly to growing interest in the kinetic-theoretical or statistical-mechanical foundation of transport phenomena, partly to practical or industrial motivations regarding electrochemistry, limits of measurement, electronic noise, or magnetic nuclear resonance. Concepts and methods traveled between practical fields and lofty theory. For instance, the theories of Brownian motion and Onsager's fluctuation-based derivation of the reciprocal relations have deep roots in late nineteenth-century electrochemistry, and Callen's theorems relied on methods of circuit theory. Some actors of this history, especially Einstein and Onsager, worked out their main ideas individually. Others like Callen and Kubo had a marked individuality but also profited from collaborations. Nyquist was working for a large corporation, AT&T. In Japan, Kubo benefitted from the growing strength of a Tokyo research group on what we would now call many-body physics.