Special Relativity tells us that space and time are "reshuffled" every time we change frame of reference. The second law of thermodynamics, on the other hand, introduces a profound asymmetry between past and future, therefore attributing a privileged role to time. Can these two facts coexist? Is it possible to combine Lorentz-invariance and the "thermodynamic arrow of time" within a consistent description? In this talk, I will show that the answer is affirmative if and only if some mathematical conditions are met. The famous "instabilities" of relativistic viscous fluid dynamics arise whenever such mathematical conditions are violated.
