Onsager Relations and Hydrodynamic Balance Equations in 2D Quantum Wells
  In this letter we clarify the role of heat flux in the hydrodynamic balance equations in 2D quantum wells, facilitating the formulation of an Onsager relation within the framework of this theory. We find that the Onsager relation is satisfied within the framework of the 2D hydrodynamic balance equation transport theory at sufficiently high density. The condition of high density is consonant with the requirement of strong electron-electron interactions for the validity of our balance equation formulation. 
M.W. Wu, H.L. Cui, W. Sun, and S.Y. Wu