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

Extended thermodynamics of heat-conducting fluids is used to give explicitformulas for non- equilibrium energy density of ideal gas expressed asfunctions of classical variables and the diffusive entropy flux (anonequilibrium variable). A Lagrangian density associated with the energydensity is used to obtain the components of energy-momentum tensor andcorresponding conservation laws on the basis of Hamilton's principle ofstationary action and Noether's theorem. The heat flux appears naturally as aconsequence of a free entropy transfer (independent of mass transfer) and amomentum transport is associated with tangential stresses resulting from thisentropy transfer. The compatibility of the present description with the kinetictheory is shown. Hamilton's principle is extended so that the flux of entropyas well as the fluxes and densities of mass are varied independently. Theconcept of thermal momentum as the derivative of the kinetic potential withrespect to the entropy flux is introduced; this quality plays a fundamentalrole in the extension of Gibbs's equation to describe a nonequilibrium fluidwith heat flux.