Violation of Onsager reciprocity in underdoped cuprates?

One of the canons of condensed matter physics is the Onsager reciprocity principle for systems in which the Hamiltonian commutes with the time-reversal operator. Recent results of measurements of the Nernst coefficient [1] in underdoped $\rm YBa_2Cu_30_{6+x}$, together with the measurements of the anisotropy of conductivity and the inferred anisotropy of the thermopower, imply that this principle is violated [2]. The probable violation and its temperature dependence are shown to be consistent with the loop-current phase which has been directly observed in other experiments. The violation is related directly to the magneto-electric symmetry of such a phase in which an applied electric field generates an effective magnetic field at right angle to it and to the order parameter vector, and vice versa.\\[4pt] [1] R. Daou \emph{et al.}, Nature {\bf 463}, 519 (2010).\\[0pt] [2] C. M. Varma, V. M. Yakovenko, A. Kapitulnik, arXiv:1007.1215