Existence of a general systematic derivation for UV-regularized information currents

Determine whether there exists a general systematic derivation to construct, for arbitrary first-order relativistic hydrodynamic theories, a UV-regularized information current Eμ and entropy production rate σ that satisfy the criteria stated in Section II—namely: (i) agreement with the first-order variation of the entropy in the infrared, (ii) the exact identity ∂μEμ + σ = 0 along all classical solutions, and (iii) timelike future-directed Eμ with σ ≥ 0 for arbitrary perturbations—and, if so, develop such a derivation.

Background

The paper introduces UV-regularized information currents Eμ and entropy production rates σ that render first-order relativistic hydrodynamic theories stable, causal, and suitable for defining fluctuation probabilities. The authors successfully construct such objects for a variety of models via case-by-case procedures.

However, they emphasize that their constructions often rely on trial and error and that, at present, there is no known general systematic method to derive Eμ and σ that satisfy the required properties for arbitrary first-order theories. Establishing such a method would significantly advance the theoretical framework and its applicability.