Related papers: Relativistic Entropy Inequality
The microscopic explanation of entropy has been challenged from both experimental and theoretical point of view. The expression of entropy is derived from the first law of thermodynamics indicating that entropy or the second law of…
Second-order dissipative hydrodynamic equations for each component of a multi-component system are derived using the entropy principle. The shear viscosity of the whole system, appearing in the equation summed-up over all components, is…
We derive the spatially homogeneous Landau equation for Maxwellian molecules from a natural stochastic interacting particle system. More precisely, we control the relative entropy between the joint law of the particle system and the…
The formulation of a dynamical theory of General Relativity, including matter, is viewed as a problem of coupling Einstein's theory of pure gravity, formulated as an action principle, to an independently chosen and well defined field theory…
A lagrangian for relativistic fluid systems with matters inside is developed using gauge principle. In the model, the gauge boson represents the fluid field in a form $A_\mu \equiv \epsilon_\mu \phi$, where $\epsilon_\mu$ contains the fluid…
Motivated by the fluid/gravity correspondence, we consider the Penrose inequality in the framework of fluid dynamics. In general relativity, the Penrose inequality relates the mass and the entropy associated with a gravitational background.…
We deal with a novel approach to formulation of the relativistic dissipative hydrodynamics by extending the so-called matching conditions widely used in the literature. The form of the non-equilibrium entropy current can be determined by…
In this paper, we consider mathematical modeling and numerical simulation of non-isothermal compressible multi-component diffuse-interface two-phase flows with realistic equations of state. A general model with general reference velocity is…
We derive relativistic hydrodynamics from quantum field theories by assuming that the density operator is given by a local Gibbs distribution at initial time. We decompose the energy-momentum tensor and particle current into nondissipative…
Considering the isentropic Euler equations of compressible fluid dynamics with geometric effects included, we establish the existence of entropy solutions for a large class of initial data. We cover fluid flows in a nozzle or in spherical…
In this work we discuss different interpretations of mass in the relativistic dynamics. A new way to introduce mass is proposed. Our way is based on the relativistic equation of motion expressed in the form of the Newton$'$s second law. In…
A general organizing principle is proposed that can be used to derive the equations of motion describing the near-equilibrium dynamics of causal and thermodynamically stable relativistic systems. The latter are found to display some new…
We develop first-principles theory of relativistic fluid turbulence at high Reynolds and P\'eclet numbers. We follow an exact approach pioneered by Onsager, which we explain as a non-perturbative application of the principle of…
We present a new derivation of the expressions for momentum and energy of a relativistic particle. In contrast to the procedures commonly adopted in textbooks, the one suggested here requires only the knowledge of the composition law for…
For the incompressible and the isentropic compressible Euler equations in arbitrary space dimension, we establish the principle of localised relative energy, thus generalising the well-known relative energy method. To this end, we adapt…
Relativistic hydrodynamics of classic plasmas is derived from the microscopic model in the limit of ideal plasmas. The chain of equations is constructed step by step starting from the concentration evolution. It happens that the energy…
In our derivation of the second law of thermodynamics from the relation of adiabatic accessibility of equilibrium states we stressed the importance of being able to scale a system's size without changing its intrinsic properties. This…
We develop a method of obtaining a hierarchy of new higher-order entropies in the context of compressible models with local and non-local diffusion and isentropic pressure. The local viscosity is allowed to degenerate as the density…
We derive a relative entropy inequality for capillary compressible fluids with density dependent viscosity. Applications in the context of weak-strong uniqueness analysis, pressureless fluids and high-Mach number flows are presented.
The conformal flow of metrics [2] has been used to successfully establish a special case of the Penrose inequality, which yields a lower bound for the total mass of a spacetime in terms of horizon area. Here we show how to adapt the…