Reciprocal Relations in Irreversible Processes. I.

Phys. Rev. 37, 405 – Published 15 February 1931
Lars Onsager


Examples of coupled irreversible processes like the thermoelectric phenomena, the transference phenomena in electrolytes and heat conduction in an anisotropic medium are considered. For certain cases of such interaction reciprocal relations have been deduced by earlier writers, e.g., Thomson's theory of thermoelectric phenomena and Helmholtz' theory for the e.m.f. of electrolytic cells with liquid junction. These earlier derivations may be classed as quasi-thermodynamic; in fact, Thomson himself pointed out that his argument was incomplete, and that his relation ought to be established on an experimental basis. A general class of such relations will be derived by a new theoretical treatment from the principle of microscopic reversibility. (§§1-2.) The analogy with a chemical monomolecular triangle reaction is discussed; in this case a a simple kinetic consideration assuming microscopic reversibility yields a reciprocal relation that is not necessary for fulfilling the requirements of thermodynamics (§3). Reciprocal relations for heat conduction in an anisotropic medium are derived from the assumption of microscopic reversibility, applied to fluctuations. (§4.) The reciprocal relations can be expressed in terms of a potential, the dissipation-function. Lord Rayleigh's "principle of the least dissipation of energy" is generalized to include the case of anisotropic heat conduction. A further generalization is announced. (§5.) The conditions for stationary flow are formulated; the connection with earlier quasi-thermodynamic theories is discussed. (§6.) The principle of dynamical reversibility does not apply when (external) magnetic fields or Coriolis forces are present, and the reciprocal relations break down. (§7.)


  • Received 8 December 1930
  • Published in the issue dated February 1931

© 1931 The American Physical Society

Authors & Affiliations

Lars Onsager

  • Department of Chemistry, Brown University


References (Subscription Required)

Authorization Required




Log In



Article Lookup
Paste a citation or DOI

Enter a citation
  1. Enter a citation to look up or terms to search.

    Ex: "PRL 112 068103", "Phys. Rev. Lett. 112, 068103", "10.1103/PhysRevLett.112.068103"