Peer review First-order relativistic hydrodynamics with an information current Lorenzo Gavassino Cambridge

This document presents a formal critical analysis of the manuscript “First-order relativistic hydrodynamics with an information current” (arXiv:2401.13852).We demonstrate that the central claims of the paper are untenable on general theoretical grounds. In particular, we show that:(i) ultraviolet positivity of a quadratic functional cannot emerge from a theory truncated at first order in derivatives;(ii) imposing a globally timelike information current violates effective field theory (EFT) closure;(iii) enforcing entropy or information current positivity at all scales breaks the infrared–ultraviolet (IR/UV) matching principle and cannot be reconciled with any consistent microscopic completion. These results are established through model-independent mathematical arguments, independent of specific hydrodynamic realizations. The analysis shows that the proposed framework does not resolve the known limitations of first-order relativistic hydrodynamics, but instead introduces ad hoc ultraviolet regulator conditions incompatible with EFT logic. We conclude that the construction of a globally positive, timelike information or entropy current cannot be derived within first-order hydrodynamics and must be regarded as a non-physical regulator choice rather than a fundamental theoretical result.