# Violations of Onsager reciprocity?

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As far as I understand it, the modern statement of Onsager reciprocity is that the linear-response transport coefficient matrix, when transposed, is equal to that of the time-reversed system (reversed external magnetic field, reversed internal magnetic order, reversed Coriolis forces, and so on). Many consider this to be the fourth law of thermodynamics.

Clifford Truesdell however famously complained of "Onsagerism", which appears to mean the (unjustified) faith in Onsager reciprocity despite what he regarded as shaky foundations: reliance on kinetic theory, and so on. And yet, the foundations of Onsager do not seem so shaky to me: 1) the fluctuation-dissipation theorem and 2) the mathematical fact that fluctuation correlations in a time-reversed system should be, well, time-reversed. Quite general and elegant, really. Might even be worth a Nobel prize.

So, my question: are there real counterexamples to Onsager? I have seen many proposed counterexamples where I thought "OK, you just failed to time-reverse your system properly." (and indeed perhaps the difficulty of proper time-reversal indicates an Onsagerism pitfall). But... is the reciprocity fundamentally flawed?

This post imported from StackExchange Physics at 2016-04-13 09:05 (UTC), posted by SE-user Nanite

edited Apr 13, 2016
to quote Truesdell "As far as I can learn, the first experimental tests of Stefan's relations were made by Dunlop & Gosting in 1955. As I read the results reported by them and others for eleven different solutions in water, they indicate that for eight systems Stefan's relations hold, that for one they are doubtful, and that for two they clearly do not hold." The reference is to P. J. Dunlop & L. J. Costing, "Interacting flows in liquid diffusion" J. Am. Chem. Soc, 77:5238-5249 A955).

This post imported from StackExchange Physics at 2016-04-13 09:05 (UTC), posted by SE-user hyportnex

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Onsager got the Nobel prize in Chemistry 1968 for the discovery of the reciprocal relations bearing his name, which are fundamental for the thermodynamics of irreversible processes.

His derivation is very general. In case of external magnetic fields or Coriolis fields, the Onsager relations must be modified since the behavior of these fields under time reversal is different. His paper L. Onsager, Reciprocal Relations in Irreversible Processes I, Phys. rev. 37 (1931), 405-426 already contains this caveat.

answered Apr 13, 2016 by (15,757 points)
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Onsager reciprocity is a funny thing. I think that some of the most cogent (and general) modern treatments of nonequilibrium processes are using the theory of Markov processes (see this blog post) of which the kinetic theory is a special case which satisfies a condition called "detailed balance," which is equivalent to Onsager reciprocity and by the way is also required to prove the fluctuation dissipation theorem. Lots of other strong things follow from detailed balance, such as Boltzmann's H theorem, which probably we shouldn't always expect to hold because there are some systems that never thermalize. Further, in systems with turbulence I have a hard time imagining something like detailed balance could hold because energy is always flowing from larger to smaller length scales and there is dissipation "at the bottom" due to the formation of singularities.

answered Nov 29, 2017 by (1,925 points)

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