Acausality in truncated Müller-Israel-Stewart-type theory

The causal-stable M\"uller-Israel-Stewart (MIS) theory is known to have a finite number of out-of-equilibrium derivative-order corrections but requires treating the viscosity tensor as a separate degree of freedom with its own equations of motion, apart from the fundamental fluid degrees of freedom like velocity and temperature. In this work, I will show that it is possible to rewrite the MIS theory only in terms of velocity and temperature, but the resultant constitutive relation for dissipation must include all orders of gradient corrections. In this work, I will argue that an all-order resummation of gradient contributions is equivalent to introducing new ``nonfluid'' degrees of freedom in the MIS theory. It will also be shown, using the relativistic quantum causality condition, that any finitely truncated order of derivative correction, however high it is, leads to a theory that is acausal, unless the corrections are infinitely summed up to all orders.