Relativistic theory of the viscosity of fluids across the entire energy spectrum (2406.18434v4)

Abstract: The shear viscosity is a fundamental transport property of matter. Here we derive a general theory of the viscosity of gases based on the relativistic Langevin equation (deduced from a relativistic Lagrangian) and nonaffine linear response theory. The proposed relativistic theory is able to recover the viscosity of non-relativistic classical gases, with all its key dependencies on mass, temperature, particle diameter and Boltzmann constant, in the limit of Lorentz factor $\gamma=1$. It also unveils the relativistic enhancement mechanism of viscosity. In the limit of ultrarelativistic fluids, the theory provides a new analytical formula which reproduces the cubic increase of viscosity with temperature in agreement with various estimates for hot dense matter and the QGP-type fluid.

• The paper derives shear viscosity using a novel relativistic Langevin equation that captures non-Markovian and memory effects.
• It introduces an analytical formula that shows a cubic temperature dependency in the ultrarelativistic regime versus traditional linear behavior.
• The study integrates a relativistic enhancement factor by incorporating the Lorentz factor to link viscosity with high-energy transport dynamics.

Overview of the Relativistic Theory of Viscosity in Fluids

The paper presents a theoretical framework to understand the shear viscosity of gases across a full energy spectrum using relativistic physics. The work builds upon existing kinetic theories and introduces a novel approach based on the relativistic Langevin equation derived from a relativistic Lagrangian. This approach highlights significant contributions to our understanding of transport properties in high-energy and exotic states of matter such as quark-gluon plasmas (QGP).

Key Contributions

• Relativistic Langevin Equation: A significant part of the paper is the derivation of the shear viscosity from a relativistic microscopic perspective by utilizing a Langevin equation adapted for relativistic dynamics. This equation accounts for temporal memory effects and non-Markovian dynamics, underlining the complexity introduced in relativistic systems.
• General Analytical Formula: The research proposes an analytical formula that encapsulates the behavior of viscosity across the energy spectrum. Specifically, the formula captures the expected cubic temperature dependency in the ultrarelativistic regime, in contrast to the linear behavior predicted by the relativistic Boltzmann equation traditionally resolved through the Chapman-Enskog approximation.
• Relativistic Enhancements: A novel aspect of the theoretical approach is the introduction of a relativistic enhancement factor concerning the momentum of particles. This incorporates the Lorentz factor into the viscosity expressions, linking it directly to relativistic effects not commonly considered in non-relativistic theories.

Implications and Future Directions

The practical implications of this research are substantial, particularly in the fields involving QGP and other high-energy states of matter. These insights enable more accurate modeling of fluid-like behaviors in extreme conditions, relevant to both astrophysical and laboratory settings. Additionally, understanding the viscosity of QGP may provide insights into other properties of the early universe and facilitate the search for new states of matter.

Future work might extend the theoretical framework to include more complex scenarios involving bulk viscosity and non-ideal fluid characteristics. Such expansions could have implications for the paper of neutron stars' interiors, where relativistic fluid dynamics are significant. Another area for potential development is the application of the framework to plasmas, considering both relativistic and non-relativistic regimes. Integrating quasi-linear theory into this relativistic framework may yield new insights into plasma behavior and further test the presented theoretical predictions.

Conclusion

The paper provides a robust framework for analyzing the viscosity of fluids at relativistic speeds, bridging a gap in our understanding of transport phenomena across different energy spectra. The analytical results, especially concerning the ultrarelativistic limit, align well with existing estimates and suggest a more nuanced understanding of momentum dissipation in such extreme conditions. This work lays a foundation for further theoretical and experimental explorations into relativistic fluid dynamics, potentially catalyzing advancements in high-energy physics and related fields.