2025/12/03 by Blaschke, David, Röpke, Gerd, Baym, Gordon
#FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Nuclear Theory (nucl-th) #Plasma Physics (physics.plasm-ph)
paper · doi:10.48550/arxiv.2512.03876
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.