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We derive causal relativistic fluid dynamical equations from the relaxation model of kinetic theory as in a procedure previously applied in the case of non-relativistic rarefied gases. By treating space and time on an equal footing and…

General Relativity and Quantum Cosmology · Physics 2011-08-03 Xinzhong Chen , Edward A Spiegel

We present a new method for imposing a realistic equation of state in anisotropic hydrodynamics. The method relies on the introduction of a single finite-temperature quasiparticle mass which is fit to lattice data. By taking moments of the…

High Energy Physics - Phenomenology · Physics 2015-11-30 Mubarak Alqahtani , Mohammad Nopoush , Michael Strickland

The hydrodynamic limit and Newtonian limit are important in the relativistic kinetic theory. We justify rigorously the validity of the two independent limits from the special relativistic Boltzmann equation to the classical Euler equations…

Analysis of PDEs · Mathematics 2023-09-01 Yong Wang , Changguo Xiao

We derive the equations of motion of relativistic magnetohydrodynamics, as well as microscopic expressions for all of its transport coefficients, from the Boltzmann equation using the method of moments. In contrast to reference Phys. Rev. D…

Nuclear Theory · Physics 2024-05-24 Khwahish Kushwah , Gabriel S. Denicol

Consistent formulations of relativistic viscous hydrodynamics involve short lived modes, leading to asymptotic rather than convergent gradient expansions. In this Letter we consider the Mueller-Israel-Stewart theory applied to a…

High Energy Physics - Theory · Physics 2015-08-31 Michal P. Heller , Michal Spalinski

Generative models based on invertible transformations provide a physics-aware route to sample equilibrium configurations directly from the Boltzmann distribution, enabling efficient exploration of complex thermodynamic landscapes. Here, we…

Statistical Mechanics · Physics 2026-03-06 Luigi de Santis , John Russo , Andrea Ninarello

The equations of continuum hydrodynamics can be derived from the Boltzmann equation, which describes rarefied gas dynamics at the kinetic level, by means of the Chapman-Enskog expansion. This expansion assumes a small Knudsen number, and as…

Statistical Mechanics · Physics 2011-10-07 Carlos Escudero

Rajagopal and Srinivasa's thermodynamic framework derives constitutive relations in continuum mechanics from two scalar functions describing energy storage and entropy production via a constrained optimization principle. In parallel,…

Mathematical Physics · Physics 2026-05-05 Patrick E. Farrell , Josef Málek , Ondřej Souček , Umberto Zerbinati

In this paper, we give a rigorous mathematical justification for the relaxation time approximation (RTA) model. We find that only the RTA with an energy-independent relaxation time can be justified in the case of hard interactions.…

High Energy Physics - Phenomenology · Physics 2026-01-28 Jin Hu

In this work we investigate the impact of conformal symmetry breaking on hydrodynamization of a far-from-equilibrium fluid. We find a new kind of transseries solutions for the non-conformal hydrodynamic equations of a longitudinal boost…

Fluid Dynamics · Physics 2023-06-21 Syo Kamata , Jakub Jankowski , Mauricio Martinez

A new kinetic theory Boltzmann-like collision term including correlations is proposed. In equilibrium it yields the one-particle distribution function in the form of a generalised-Lorentzian resembling but not being identical with the…

Plasma Physics · Physics 2009-10-31 R. A. Treumann

We derive the equations of motion for a system undergoing boost-invariant longitudinal and azimuthally-symmetric transverse "Gubser flow" using leading-order anisotropic hydrodynamics. This is accomplished by assuming that the one-particle…

Nuclear Theory · Physics 2015-02-05 Mohammad Nopoush , Radoslaw Ryblewski , Michael Strickland

We derive the equations of motion of relativistic magnetohydrodynamics from the Boltzmann equation using the method of moments. We consider a locally electrically neutral system composed of two particle species with opposite charges, with…

High Energy Astrophysical Phenomena · Physics 2026-02-25 Khwahish Kushwah , Gabriel Silveria Denicol

We introduce a novel approach to study the longitudinal hydrodynamic expansion of the quark-gluon fluid created in heavy-ion collisions. It consists of two steps: First, we apply the maximum entropy method to reconstruct the freeze-out…

Nuclear Theory · Physics 2014-04-24 Mikhail Stephanov , Yi Yin

We present the first numerical analysis of causal, stable first-order relativistic hydrodynamics with ideal gas microphysics, based in the formalism developed by Bemfica, Disconzi, Noronha, and Kovtun (BDNK theory). The BDNK approach…

General Relativity and Quantum Cosmology · Physics 2023-01-03 Alex Pandya , Elias R. Most , Frans Pretorius

We generalize a recent prescription for the relaxation time approximation for the relativistic Boltzmann equation for systems with multiple particle species at finite temperature. This is performed by adding counter-terms to the traditional…

Nuclear Theory · Physics 2025-10-21 Gabriel S. Rocha , Gabriel S. Denicol

In this paper, explicit method of constructing approximations (the Triangle Entropy Method) is developed for nonequilibrium problems. This method enables one to treat any complicated nonlinear functionals that fit best the physics of a…

Statistical Mechanics · Physics 2016-08-31 A. N. Gorban , I. V. Karlin

We establish the anisotropic hydrodynamics (aHydro) equations based on a boost-non-invariant longitudinally expanding system. Good consistency is found in the comparison between the aHydro results with those from the Boltzmann equation…

Nuclear Theory · Physics 2024-10-01 Shile Chen , Shuzhe Shi

We review the key steps of the relativistic fluid dynamics formalism with spin degrees of freedom initiated recently. We obtain equations of motion of the expansion of the system from the underlying definitions of quantum kinetic theory for…

Nuclear Theory · Physics 2021-04-06 Rajeev Singh

We study the far-off-equilibrium dynamics of a Bjorken expanding non-conformal system within kinetic theory and hydrodynamics. We show that, in contrast to the conformal case, neither shear nor bulk viscous pressure relax quickly to a…

Nuclear Theory · Physics 2022-08-02 Sunil Jaiswal , Subrata Pal , Chandrodoy Chattopadhyay , Lipei Du , Ulrich Heinz