Invalidity of Meixner's theorem in irreversible thermodynamics

Re Nettleton
1962 Journal of Research of the National Bureau of Standards Section B Mathematics and Mathematical Physics  
Meixner 's theorem, on the preservat ion of t he Onsager symmetry of phenomenological coe ffici ents under transformations of forces and fluxes which leave the rate of entropy production innll'iant, is shown to be invalid under the restricti on that all fluxe s be even or odd ullder t ime-reversal and t hat the phenomenological equations be yalid fol' \'ery s hort ti tTles. This result extends an earlier proof of Coleman a nd Truesdell, whose proof does not impose these t wo restriction s. A
more » ... formulation of ::'I1eixner's t heorem is t hus shOIl-n to be requ ired, and this is \nitte n dO\nl together \rith a st ate ment of Onsager's theorem II-hich is consiste nt II-ith it. , X,«t) is fI notation which refers to a n ense mble average <X.(P ,Q» ofsom' function of the eoordinales Q a nd momenta P of all the molecules in the system. 'rhe transform ation t -t means reversal of the s ig ns of the momenta inside the ang ul al' bracket. ' 13_ D . Cole man ancl C. Truesdell , J_ Chern . Phys. 33.28 (1960). 6 Statem en t I has bee n shown to hold , b y S. R. dcO root an d P. M az ur, Phys. Rev. 94,21 8, 224 ( 1954), in special cases of heat cond uction and clilTusion, but th is demonstration cannot be automatica ll y extended to cases where gradients of temperature or concentration are co upled in thc phcnomcnological equations with forces of the type oS/ey •.
doi:10.6028/jres.066b.013 fatcat:zqjnzja4jrectjkauxq42ghvky