Relativistic theory of the viscosity of fluids across the entire energy spectrum

The shear viscosity is a fundamental transport property of matter. Here we derive a general theory of the viscosity of gases based on the relativistic Langevin equation (deduced from a relativistic Lagrangian) and nonaffine linear response theory. The proposed relativistic theory is able to recover the viscosity of nonrelativistic classical gases, with all its key dependencies on mass, temperature, particle diameter, and Boltzmann constant, in the limit of Lorentz factor γ=1. It also unveils the relativistic enhancement mechanism of viscosity. In the limit of ultrarelativistic fluids, the theory provides an analytical formula which reproduces the cubic increase of viscosity with temperature in agreement with various estimates for hot dense matter and the quark-gluon-plasma-type fluid.