相对论连续介质力学的熵表述
Entropic formulation of relativistic continuum mechanics
摘要：
在Landau-Lifshitz框架下建立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，一个是小尺度，表示每个物质粒子的线性尺寸，另一个是大尺度，表示由物质粒子组成的大系统的线性尺寸，并线性回归到平衡态。我们提出了一个局部泛函，期望代表更大系统的总熵，并要求在线性回归过程中熵泛函最大化。我们表明，Onsager的原始想法，线性回归，然后可以实现明确的耗散电流在所需的形式与电流守恒。我们证明了这种配方的有效性，表明可以处理一个广泛的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。
英文摘要：
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 the 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.
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