Convective variational approach to relativistic thermodynamics of dissipative fluids
Convective variational approach to relativistic thermodynamics of dissipative fluids
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耗散流体相对论热力学的对流变分法
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发表时间：
1991
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通讯作者：
B. Carter
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作者：
B. Carter
使用由对流类型的广义变分过程所产生的诺特恒等式提供的指导方针，开发了一种新的（非线性和完全自洽的）相对论热力学模型类别，用于粘性导电流体介质的系统表示（允许几个独立的带电或中性化学成分）。除了提供一组通常的耗散系数外，（反应性、电阻率和粘度）类型，特定模型的规格仅通过给出对相关动力学变量的单个“主函数”（例如，Δ）的代数依赖性来确定，其在此被假定由对应于各种化学成分的熵流4矢量和一组粒子流4矢量组成，连同一组对称（秩3）粘性张量，其被认为是动态地独立于相应的电流矢量，除了在线性粘性的退化极限。主函数被设置为一个普通的拉格朗日函数，它减少到相关的非耗散极限的推广，并在保守的情况下，它是用于建设衍生的数量在这样一种方式，适当的自洽条件满足的身份。特别地，直接根据独立变量和它们的动力学共轭获得了相关的应力-动量-能量张量（其作用隐藏在Israel和Stewart开发的传统方法中），这些方法是普通的4-动量集（不是4-动量密度）与独立电流相关的共矢量，和一组广义柯西型应变（不是应变率）张量与独立的粘性应力贡献。以这种方式获得的范畴的应用范围旨在包括标准（Israel-Stewart）形式主义的应用范围，在热力学平衡的足够小的偏差的限制下，它被期望有效地等价于标准形式主义。
Using guidelines provided by Noether identities arising from a generalized variation procedure of convective type, a new (nonlinear and exactly self-consistent) category of relativistic thermodynamic models is developed for the systematic representation of viscous conducting fluid media (allowing for several independent charged or neutral chemical constituents). Apart from the provision of a set of dissipation coefficients of the usual (reactivity, resistivity, and viscosity) type, the specification of a particular model is determined just by giving the algebraic dependence a single ‘master function’, ͘Λ say, on the relevant dynamical variables, which are supposed here to consist of an entropy current 4-vector and a set of particle current 4-vectors corresponding to the various chemical constituents, together with a set of symmetric (rank 3) viscosity tensors, which are considered as being dynamically independent of the corresponding current vectors except in the degenerate limit of linear viscosity. The master function is set up as a generalization of an ordinary lagrangian function, to which it reduces in the relevant non - dissipative limit, and, as in the conservative case, it is used for the construction of derived quantities in such a way that appropriate self-consistency conditions are satisfied as identities. In particular the relevant stress-momentum-energy tensor is obtained directly in terms of the independent variables and of their dynamical conjugates (whose role is hidden in the traditional approach as developed by Israel & Stewart), which are set of ordinary 4-momentum (not 4-momentum density) covectors associated with the independent currents, and a set of generalised Cauchy type strain (not strain - rate) tensors associated with the independent viscous stress contributions. The range of application of the category obtained in this way is intended to include that of the standard (Israel-Stewart) formalism to which it is expected to be effectively equivalent in the limit of sufficiently small deviations from thermodynamic equilibrium.