Conservation laws from Hamilton’s principle for nonlocal thermodynamic equilibrium fluids with heat flow

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Abstract
Extended thermodynamics of heat-conducting fluids is used to give explicit formulas for non- equilibrium energy density of ideal gas expressed as functions of classical variables and the diffusive entropy flux (a nonequilibrium variable). A Lagrangian density associated with the energy density is used to obtain the components of energy-momentum tensor and corresponding conservation laws on the basis of Hamilton’s principle of stationary action and Noether’s theorem. The heat flux appears naturally as a consequence of a free entropy transfer (independent of mass transfer) and a momentum transport is associated with tangential stresses resulting from this entropy transfer. The compatibility of the present description with the kinetic theory is shown. Hamilton’s principle is extended so that the flux of entropy as well as the fluxes and densities of mass are varied independently. The concept of thermal momentum as the derivative of the kinetic potential with respect to the entropy flux is introduced; this quality plays a fundamental role in the extension of Gibbs’s equation to describe a nonequilibrium fluid with heat flux.

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