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The Quark Gluon Plasma produced in heavy-ion collisions has three relevantconserved charges: baryon number (B), strangeness (S), and electric charge (Q).Here we derive the Israel-Stewart framework for BSQ diffusion coupled to shearand bulk viscosity and the thermodynamic derivatives needed to couple this to aBSQ equation of state. We reproduce a subset of the ${\mathcal{J}}$ terms inthe DNMR approach and propose a technique to derive other terms from themaximum entropy principle. Finally, we preform a stability analysis that can beused to constraint transport coefficients in BSQ hydrodynamics.

Stability of multi-component relativistic viscous hydrodynamics from Israel-Stewart and reproducing DNMR from maximizing the entropy