Self-consistent approximations in relativistic plasmas: Quasiparticle analysis of the thermodynamic properties

We generalize the concept of conserving, Phi-derivable, approximations to relativistic field theories. Treating the interaction field as a dynamical degree of freedom, we derive the thermodynamic potential in terms of fully dressed propagators, an approach which allows us to resolve the entropy of a relativistic plasma into contributions from its interacting elementary excitations. We illustrate the derivation for a hot relativistic system governed by electromagnetic interactions.