A quantum story of equations of state and Harmonic numbers

In this talk I will discuss how thermodynamic equations of state are encoded in quantum field theory. Through a simple concrete example, I will show how these can be derived in a Feynman diagrammatic approach, and discuss how the calculation of the thermal loops that emerge out of this expansion can be made efficient by adopting number-theoretical methods based on Mellin transforms. Curiously, the resulting expressions suggest that it should be possible to measure Harmonic and other notable numbers in a lab experiment.