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Relativistic Dissipative Hydrodynamics: A Minimal Causal Theory

T. Koide, G. S. Denicol, Ph. Mota, T. Kodama

TL;DR

The paper addresses acausality in relativistic dissipative hydrodynamics by proposing a minimal causal theory that uses a memory function with a single relaxation time $\tau_R$ to render the dynamics hyperbolic. Dissipative currents are given by time-nonlocal integrals of the ideal-fluid variables, which transform into differential equations and simplify 3D implementation compared to Israel-Stewart. The framework preserves the standard thermodynamic variables and yields results in Bjorken flow that closely resemble IS in the appropriate regime, while offering a streamlined structure and straightforward coupling to existing hydrodynamic codes. Entropy production is discussed with a relaxed nonnegativity requirement, valid in near-equilibrium timescales, and the approach is positioned as readily applicable to QGP phenomenology and 3D simulations.

Abstract

We present a new formalism for the theory of relativistic dissipative hydrodynamics. Here, we look for the minimal structure of such a theory which satisfies the covariance and causality by introducing the memory effect in irreversible currents. Our theory has a much simpler structure and thus has several advantages for practical purposes compared to the Israel-Stewart theory (IS). It can readily be applied to the full three-dimensional hydrodynamical calculations. We apply our formalism to the Bjorken model and the results are shown to be analogous to the IS.

Relativistic Dissipative Hydrodynamics: A Minimal Causal Theory

TL;DR

The paper addresses acausality in relativistic dissipative hydrodynamics by proposing a minimal causal theory that uses a memory function with a single relaxation time to render the dynamics hyperbolic. Dissipative currents are given by time-nonlocal integrals of the ideal-fluid variables, which transform into differential equations and simplify 3D implementation compared to Israel-Stewart. The framework preserves the standard thermodynamic variables and yields results in Bjorken flow that closely resemble IS in the appropriate regime, while offering a streamlined structure and straightforward coupling to existing hydrodynamic codes. Entropy production is discussed with a relaxed nonnegativity requirement, valid in near-equilibrium timescales, and the approach is positioned as readily applicable to QGP phenomenology and 3D simulations.

Abstract

We present a new formalism for the theory of relativistic dissipative hydrodynamics. Here, we look for the minimal structure of such a theory which satisfies the covariance and causality by introducing the memory effect in irreversible currents. Our theory has a much simpler structure and thus has several advantages for practical purposes compared to the Israel-Stewart theory (IS). It can readily be applied to the full three-dimensional hydrodynamical calculations. We apply our formalism to the Bjorken model and the results are shown to be analogous to the IS.

Paper Structure

This paper contains 7 sections, 73 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Diffusion Equation and Acausality
  3. Minimal Causal Hydrodynamics
  4. Entropy Production
  5. One-Dimensional Scaling Solution
  6. Solutions
  7. Summary and Concluding remarks

Figures (2)

  • Figure 1: The time evolution of the energy density. The dashed curves correspond to the calculations with the constant viscosity and relaxation time. The first two lines from the top represent the results of the LL. Next two lines shows the results of our theory. The last line is the result of ideal hydrodynamics.
  • Figure 2: The time evolution of energy density with the different initial conditions from Fig. 1. The dashed and short dashed lines represent the result of the LL and our theory, respectively . For comparison, our result of Fig. 1 is shown, again (ideal $T^{\mu\nu}(\tau_0)$). The last line from the top is the result of ideal hydrodynamics. In this case, the energy heat-up is observed even in our theory.