Though they arose in Onsager's mind from his studies of electrolytic conduction, he soon recognized their application to the cross-coefficients for the diffusion of pairs of solutes in the same solution (1932,1) and the varied interactions that can occur between thermal conduction, diffusion, and electrical conduction.

Thermal diffusion was an important special case: the temperature gradients set up by the interdiffusion of two gases have their counterpart in the partial separation that occurs when a temperature gradient is applied to a mixture of gases. At the beginning of World War II Onsager published two important papers on this subject (1939,2 and 1940,1). In a comprehensive review of the experimental evidence several years later, D. G. Miller¹³ concluded that the reciprocal relations were obeyed, within experimental error, in all the varied physical situations in which they had yet been checked. Eight years later still, they earned their discoverer the Nobel Prize.

Onsager himself set much store by the Principle of Least Dissipation, which—for systems very close to equilibrium—he showed to be mathematically equivalent to the reciprocal relations. The passage of time has perhaps modified this judgment; though the Principle was later generalized by Onsager and Machlup (1953,1,2) and supplied with new theoretical foundations, it does not in fact hold for substantial departures from equilibrium and, in any case, it is the reciprocal relations that are directly accessible to experimental test.

Onsager remained at Brown until 1933, when the economic depression made it necessary for his appointment to be discontinued. It would have been impossible for the Chemistry Department to convince the University that his services as a teacher were indispensable.