Entropic formulation of relativistic continuum mechanics
Entropic formulation of relativistic continuum mechanics
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DOI：
10.1103/physreve.84.026315
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发表时间：
2011-08-15
影响因子：
2.4
通讯作者：
Sakatani, Yuho
中科院分区：
文献类型：
--
作者：
Fukuma, Masafumi;Sakatani, Yuho
在Landau-Lifshitz标架下，发展了相对论连续介质力学的熵公式。我们引入了两个空间尺度，一个是表示每个物质颗粒的线性尺寸的小尺度，另一个是表示由材料颗粒组成的、线性回归到平衡的大系统的线性尺寸的大尺度。我们提出了一个局部泛函，它被期望表示大系统的总熵，并要求在线性回归过程中使熵泛函最大化。我们证明了Onsager关于线性回归的原始思想可以显式地实现为具有所需形式的耗散电流的电流守恒。我们通过证明这一公式的有效性，表明人们可以处理一大类相对论连续介质材料，包括标准的相对论粘性流体和相对论粘弹性材料。
An entropic formulation of relativistic continuum mechanics is developed in the Landau-Lifshitz frame. We introduce two spatial scales, one being the small scale representing the linear size of each material particle and the other the large scale representing the linear size of a large system which consists of material particles and is to linearly regress to the equilibrium. We propose a local functional which is expected to represent the total entropy of the larger system and require the entropy functional to be maximized in the process of linear regression. We show that Onsager's original idea on linear regression can then be realized explicitly as current conservations with dissipative currents in the desired form. We demonstrate the effectiveness of this formulation by showing that one can treat a wide class of relativistic continuum materials, including standard relativistic viscous fluids and relativistic viscoelastic materials.