A theoretical preprint suggests that two ways of describing a relativistic fluid can assign different values to thermal conductivity while producing the same calculated damping of sound. The result comes from an analytic model, not from measurements, and applies to the specific conditions examined in the study.
The paper compares the Eckart and Landau–Lifshitz frame conventions. In the Eckart description, the fluid is defined so that there is no particle diffusion; in the Landau–Lifshitz description, there is no energy diffusion. The study asks whether that choice changes transport-coefficient values while leaving physical observables unchanged when the equations are handled consistently.
Two descriptions of the same model
The analysis is restricted to second-order Müller–Israel–Stewart hydrodynamics, referred to in the paper as the MIS framework. The modeled system is a baryon-rich relativistic fluid described with a Boltzmann nucleon-gas equation of state, which supplies the thermodynamic relations used in the calculations.
There is no empirical sample in the analysis. Instead, the researchers derive how fluid variables and transport coefficients transform between the two frames, then compare the resulting hydrodynamic modes for the same thermodynamic model and perturbation setup. Sound propagation is studied by linearizing longitudinal modes around equilibrium.
The frame conversion leaves number density exactly equal between the two descriptions in the stated transformation. Energy density and pressure are reported to differ only at second order in dissipative quantities, so the leading-order thermodynamic description agrees between frames within the model.
Conductivity is frame-specific
The clearest difference concerns thermal conductivity. The paper derives a multiplicative thermodynamic relation between the conductivity used in the Eckart frame and the one used in the Landau–Lifshitz frame. In practical terms, a conductivity value cannot be compared across the two conventions without accounting for the frame transformation.
In the Boltzmann nucleon-gas calculation, the Landau–Lifshitz conductivity is lower than the Eckart value. The ratio between the frame-specific conductivities increases across the reported scans of baryon chemical potential and temperature. These are deterministic model results; the analysis reports no confidence intervals or other statistical uncertainty estimates.
The authors interpret the difference as a repartition of heat flow and particle diffusion between the two descriptions. On that reading, the conductivity shift reflects how the dissipative currents are defined in each frame rather than a change in the underlying transport physics.
Sound attenuation remains unchanged in the calculation
The study then tests sound attenuation, the damping of a sound disturbance in the modeled fluid. It obtains the hydrodynamic modes from a dispersion relation after linearizing longitudinal motion, allowing the two frame descriptions to be compared within the same perturbative setup.
The long-wavelength analysis produces three hydrodynamic branches, including two propagating sound modes. The damping of those sound modes contains contributions from viscous dissipation and baryon diffusion, so the comparison includes more than viscosity alone.
Despite the different conductivity values, the sound attenuation coefficient is reported as identical in the Eckart and Landau–Lifshitz descriptions. The authors take that agreement as evidence that physical observables remain invariant when the frame transformation is applied consistently within the same model.
What the result does—and does not—settle
The finding is useful mainly as a warning about terminology and comparison. A transport coefficient that appears in one hydrodynamic frame may not have the same numerical value in another, even when both descriptions refer to the same modeled fluid. Sound attenuation offers a more frame-invariant comparison in this analysis.
The result does not establish that changing the frame changes a microscopic transport mechanism, and it does not show that the relations hold in experimental systems. The evidence is limited to the specified second-order framework, the baryon-rich Boltzmann nucleon-gas equation of state, and the linearized, long-wavelength treatment around equilibrium.
The analysis also reports no uncertainty intervals, sensitivity analysis, or inferential statistical tests. That is consistent with its design as a deterministic theoretical calculation rather than an empirical study, but it means the paper does not quantify uncertainty in the way a data-based result would.
Whether the frame relations persist for other equations of state, interacting or multicomponent fluids, or regimes farther from equilibrium remains open. The supplied text also contains a visibly garbled term in one derivation, Eq. (76), which limits verification of that line and warrants independent checking of the transport-coefficient calculation.
The preprint, dated 20 Aug 2026, provides explicit expressions in an appendix for the relaxation parameters and thermo-viscous coupling coefficients used in the MIS equations. It also reports analogous constant translations for those second-order coefficients, extending the frame comparison beyond thermal conductivity.
The supplied front matter lists the authors and affiliations but contains no funding statement. No empirical dataset is reported, because the work is based on analytic expressions and model calculations.
Paper data and sources
Original title: Correspondence between hydrodynamic frames, transport coefficients, and hydrodynamic modes in relativistic fluids
Authors: Md Hasanujjaman, Mahfuzur Rahaman
Journal/Repository: arXiv
Status: Preprint, not yet peer-reviewed
First online: 2026-08-20
DOI: Not available
Original paper · Full text