Deviations From the Linear Transport Laws and Corrections to the Onsager Reciprocal Relations

[+] Author and Article Information
W. A. Scheffler

Department of Mechanical and Chemical Engineering, Joint Center for Graduate Study, Richland, Wash.

J. S. Dahler

Chemical Engineering Department, University of Minnesota, Minneapolis, Minn.

W. E. Ibele

Mechanical Engineering Department, University of Minnesota, Minneapolis, Minn.

J. Appl. Mech 43(3), 409-413 (Sep 01, 1976) (5 pages) doi:10.1115/1.3423881 History: Received October 01, 1974; Revised November 01, 1975; Online July 12, 2010


An extension of the linear transport laws is derived from first principles of statistical mechanics. The resulting transport laws include both relaxation and nonlinear terms. It is found when these terms are included the Onsager reciprocal relations are no longer valid. Therefore, the development gives the limit of validity of the Onsager relations, as well as expressing the transport coefficients as correlation functions of the dynamical variables. In order to show the validity of the procedure used, a functional integral is derived as a first-order approximation for the transition probability. This integral when evaluated verifies the assumption of Onsager and Machlup for the transition probability for the linear transport laws.

Copyright © 1976 by ASME
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