We discuss a puzzle in relativistic spin hydrodynamics; in the previous formulation the spin source from the antisymmetric part of the canonical energy-momentum tensor (EMT) is crucial. The Belinfante improved EMT is pseudo-gauge transformed from the canonical EMT and is usually a physically sensible choice especially when gauge fields are coupled as in magnetohydrodynamics, but the Belinfante EMT has no antisymmetric part. We find that pseudo-transformed entropy currents are physically inequivalent in nonequilibrium situations. We also identify a current induced by the spin vorticity read from the Belinfante symmetric EMT.

中文翻译：

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自旋流体力学和对称的能量动量张量–由自旋涡度感生的电流–

我们讨论了相对论自旋流体动力学中的一个难题。在先前的公式中，来自规范能量动量张量（EMT）的反对称部分的自旋源至关重要。Belinfante改进的EMT是从规范EMT转换而来的伪规范，通常是一种物理上明智的选择，尤其是在磁流体动力学耦合规范磁场的情况下，但是Belinfante EMT没有反对称部分。我们发现伪变换的熵电流在非平衡情况下在物理上是不等价的。我们还确定了由Belinfante对称EMT读取的自旋涡旋感生的电流。