Onsager relations and hydrodynamic balance equations

TL;DR

This paper demonstrates that the Onsager reciprocal relations hold within hydrodynamic balance equations for high-density electron systems, clarifying the role of heat flux and extending the theory's applicability.

Contribution

It verifies the Onsager relation within the balance equation framework, previously thought unattainable, for high-density electron systems and discusses extensions to non-equilibrium conditions.

Findings

Onsager relations are satisfied in high-density regimes.

Balance equations accurately predict linear flux responses.

Supports validity of balance equations for weakly nonuniform systems.

Abstract

In this paper we clarify the role of heat flux in the hydrodynamic balance equations, facilitating the formulation of an Onsager relation within the framework of this theory. Previously thought to be unobtainable from the present form of the theory [X.L. Lei, J. Cai, and L.M. Xie, Phys. Rev. B {\bf 38},1529 (1988)], our verification of the Onsager relation for linear particle and heat flux currents driven by electric fields and temperature gradients resolves a puzzling issue of long standing. Our results show that, for any temperature, when electron density is sufficiently high, the linear predictions of balance equation theory exactly satisfy the Onsager relation. The condition of high density is consonant with the requirement of strong electron-electron interactions for the validity of the Lei-Ting balance equations. Our results support the validity of this theory for a weakly nonuniform system. We also discuss a possible method of extending this theory to a system further removed from thermal equilibrium.