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Summary

The research investigates the causal framework of truncated Müller–Israel–Stewart (MIS) hydrodynamic theory to show that all limited derivative correction sets produce non-causal results. The author shows that MIS theory can be reformulated purely in terms of velocity and temperature, but only at the cost of introducing an infinite series of gradient corrections. The main contribution demonstrates that all-order gradient resummation creates new non-fluid degrees of freedom which makes it equivalent to reintroducing these additional variables. The research findings from this study help scientists understand better the reasons which make relativistic hydrodynamics need either additional physical components or infinite mathematical terms instead of using truncated series of finite order.

Major issues

The new "non-fluid" freedom exists as a concept which people struggle to interpret in physical terms. The paper needs further explanation to show which operating modes serve as physical system excitation sources or memory storage functions or auxiliary system variable roles. The formal results need physical understanding to explain their relationship with physical systems because readers must understand this connection.

The paper assumes substantial prior familiarity with MIS theory and relativistic hydrodynamics. The document requires an additional section which demonstrates the standard use of truncation schemes through physical assumptions to help readers understand their operation without compromising scientific precision.

The manuscript needs to show its connection to current causal hydrodynamic frameworks and other resummation methods through a detailed comparison which would establish its position in the existing research field.

Minor issues

The argument needs better organization through a brief summary of its main points and conclusions which should appear at the end of the introduction section.

The text contains multiple sections which require additional explanations between them to create a better reading experience.

The technical sections require only fundamental language modifications and stylistic changes to enhance their reader comprehension.

Competing interests

The author declares that they have no competing interests.

Use of Artificial Intelligence (AI)

The author declares that they used generative AI to come up with new ideas for their review.