Speaker
Description
We develop a family of thermodynamic models for fluid systems based on a virial expansion of the internal energy in terms of the volume density. We prove that the models, formulated for systems with finite number of degrees of freedom $N$, are exactly solvable to any expansion order, as expectation values of physical observables are determined from solutions to nonlinear C-integrable PDEs of hydrodynamic type. In the large $N$ limit, phase transitions emerge as classical shock waves in the space of thermodynamic variables. Near critical points, we argue that the volume density exhibits a scaling behavior consistent with the Universality Conjecture in viscous transport PDEs. As an application, we employ our framework to nuclear/quark matter and construct a family of equations of state for the global QCD phase diagram revealing both the nuclear liquid-gas and hadron gas–QGP transitions. We demonstrate how finite-size effects smear critical signatures and shift the loci of phase boundaries via the viscous terms. Our findings indicate the importance of finite-size effects in the ongoing search for the QCD critical point via small systems created in heavy-ion collisions.
