Onsagerʹs symmetry in the Burnett regime

The Onsager Symmetry Relations (OSR), which are of fundamental importance in Linear Irreversible Thermodynamics (LIT), are not obeyed by the linearized Burnett equations for a dilute gas. In this paper we present a solution to this problem, which consists of an enlargement of the space of relevant variables to include the heat flux and the viscous tensor as state variables besides the usual conserved ones, an ansatz which has a kinetic foundation in the Gradʹs method of solution to the Boltzmann equation. After showing that the evolution equations for the non-conserved moments reduce to the usual constitutive relations for the Burnett approximation, we prove that the resultant set of hydrodynamical equations indeed satisfy the OSR.