Given the exact S-matrix of a theory, what are the thermodynamic properties of the system?
On-shell S-matrix methods enable the calculation of the QCD S-matrix to very high orders; how can this information be utilized to determine the equation of state of QCD?
Modern S-matrix bootstrap and positivity approaches constrain Effective Field Theories (EFTs) by examining consistency conditions of the S-matrix, without relying on an explicit Action formulation.
How can we derive thermodynamic information (partition function, heat capacity, speed of sound, etc) for these systems while bypassing the Action formulation?
In this talk, I will review my upcoming work addressing these questions.