S-matrix formulation of thermodynamics with N-body scatterings

Understand

We apply a phase space expansion scheme to incorporate the N-body scattering processes in the S-matrix formulation of statistical mechanics.

• A generalized phase shift function suitable for studying the thermal contribution of $N \rightarrow N$ processes is motivated and examined in various models.
• Using the expansion scheme, we revisit how the hadron resonance gas model emerges from the S-matrix framework, and consider an example of structureless scattering in which the phase shift function can be exactly worked out.
• Finally we analyze the influence of dynamics on the phase shift function in a simple example of 3- and 4-body scattering.