Generalized Beth–Uhlenbeck Entropy Formula From the Φ‐Derivable Approach

ABSTRACT We derive a generalized Beth–Uhlenbeck formula for the entropy of a dense fermion system with strong two‐particle correlations, including scattering states and bound states. We work within the Φ‐derivable approach to the thermodynamic potential. The formula takes the form of an energy‐momentum integral over a statistical distribution function times a unique spectral density. In the near mass‐shell limit, the spectral density reduces, contrary to naïve expectations, not to a Lorentzian but rather to a “squared Lorentzian” shape. The relation of the Beth–Uhlenbeck formula to the Φ‐derivable approach is exact at the two‐loop level for Φ. The formalism we develop, which extends the Beth–Uhlenbeck approach beyond the low‐density limit, includes Mott dissociation of bound states, in accordance with Levinson's theorem, and the self‐consistent back reaction of correlations in the fermion propagation. We discuss applications to further systems, such as quark matter and nuclear matter.