论文标题
理想气体的外壳拉格朗日
On-shell Lagrangian of an ideal gas
论文作者
论文摘要
在一般相对性的背景下，能量和线性动量约束都导致了相同的方程式，以在同质和各向同性的Friedmann-Lema- Robertson-Walkson-Walker-Walker Universe中具有固定质量和结构的游离局部粒子的速度演变。在本文中，我们通过在重力理论非最小程度地耦合到物质的背景下考虑颗粒和流体的动力学来扩展此结果。我们表明，无论先前关于物质领域的壳lagrangian的形式的任何先前假设，都可以获得粒子线性动量演变的方程。我们还发现，颗粒的能量演变和线性动量之间的一致性要求它们的体积平均在壳上散布的Lagrangian和能量 - 能量张量痕迹痕量重合（$ \ MATHCAL L _ {\ rm rm in shell on-shell on-shell} = t $）。我们进一步证明，同样的是由许多这样的颗粒组成的理想气体。该结果意味着文献中的两个最常见的假设是完美液体的壳拉格朗日（$ \ \ \ \ \ \ \ \ rm {\ rm on-shell} = \ Mathcal {p} $和$ \ Mathcal l _ {\ Mathcal l _ {\ rm on-Shell on-shell on-shell} = - $ρ$，$ρ$ at $ρ$ pp \ ats $ρ$ etc {除了灰尘（在这种情况下$ t =-ρ$）外，分别不适用于理想气体。
In the context of general relativity, both energy and linear momentum constraints lead to the same equation for the evolution of the speed of free localized particles with fixed proper mass and structure in a homogeneous and isotropic Friedmann-Lemaître-Robertson-Walker universe. In this paper we extend this result by considering the dynamics of particles and fluids in the context of theories of gravity nonminimally coupled to matter. We show that the equation for the evolution of the linear momentum of the particles may be obtained irrespective of any prior assumptions regarding the form of the on-shell Lagrangian of the matter fields. We also find that consistency between the evolution of the energy and linear momentum of the particles requires that their volume-averaged on-shell Lagrangian and energy-momentum tensor trace coincide ($\mathcal L_{\rm on-shell}=T$). We further demonstrate that the same applies to an ideal gas composed of many such particles. This result implies that the two most common assumptions in the literature for the on-shell Lagrangian of a perfect fluid ($\mathcal L_{\rm on-shell}=\mathcal{P}$ and $\mathcal L_{\rm on-shell}=-ρ$, where $ρ$ and $\mathcal{P}$ are the proper density and pressure of the fluid, respectively) do not apply to an ideal gas, except in the case of dust (in which case $T=-ρ$).
