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The recently proposed connection between the Lorentz invariance of stabilityand the speed of signal propagation has been tested for a first-orderrelativistic dissipative hydrodynamic theory. The fact that the stabilitysituation in different reference frames agrees with each other only as long asthe signal propagation respects causality, has been explicitly established forthe theory, which is microscopically derived from the covariant kineticequation in general hydrodynamic frames with arbitrary momentum-dependentinteractions.

An expedition to the islands of stability in the first-order causal hydrodynamics