EQUATION OF STATE FOR COOL RELATIVISTIC 2-CONSTITUENT SUPERFLUID DYNAMICS

The natural relativistic generalization of Landau's two-constituent superfluid theory can be formulated in terms of a Lagrangian scrL that is given as a function of the entropy current four-vector sρ and the gradient ρcphi of the superfluid phase scalar. It is shown that in the ''cool'' regime, for which the entropy is attributable just to phonons (not rotons), the Lagrangian function scrL{s→,cphi} is given by an expression of the form scrL=P-3ψ where P represents the pressure as a function just of ρcphi in the (isotropic) cold limit. The entropy current-dependent contribution ψ represents the generalized pressure of the (nonisotropic) phonon gas, which is obtained as the negative of the corresponding grand potential energy per unit volume, whose explicit form has a simple algebraic dependence on the sound or ''phonon'' speed cP that is determined by the cold pressure function P. © 1995 The American Physical Society.