Variational relativistic thermohydrodynamics
Stanislaw Sieniutycz
Working with continua at hydrodynamic level we postulate that general conservation laws are independent of irreversible phenomena. We show that this independence holds in the system’s own state space and enables one to apply the reversible Hamilton’s principle in order to find conservation laws for energy and momentum in imperfect systems. A general relativistic Lagrangian is constructed which yields the effect of
heat flux, q, and nonequilibrium stress, τ , in the energymomentum tensorGof an extended reversible fluid exhibiting thermal inertia. Extended Hamilton principle is applied that admits thermal degrees of freedom (entropy four-flux) and yields G as the tensor source of the gravitational field. For the instantaneous properties of this field it is inessential whether the origins of heat flux, q, and of nonequilibrium stress, τ in G are reversible or not, the property which makes G directly applicable to real dissipative fluids. Relativistic transformations for temperature and chemical potentials in moving continua composed of phonons or massive particles are discussed in the light of kinetic potentials and theory of thermodynamic transformations.
CYBERNETICS AND PHYSICS, Vol. 3, No. 4. 2014, 180-193.