标题： 从 kinetic 理论中没有速度不变性的流体力学：从完美流体到活动群体 显示英文标题

标题： Hydrodynamics without Boost-Invariance from Kinetic Theory: From Perfect Fluids to Active Flocks

摘要： 我们从kinetic theory（动理论）推导出无boost不变性的完美流体的流体力学方程[1]。 我们的方法是遵循基于一个先验未知的满足某些公理性质的碰撞泛函的标准Vlasov层次结构推导。动理论处理使我们能够在流体力学范围内识别各种输运系数。 我们识别出一种漂移项，它导致一种弛豫到一个平衡态，其中关于动量传递与环境之间的详细平衡得以实现。 然后我们展示如何从boost非不变性的动理论和流体力学中恢复鸟群流体力学的导数展开。 我们识别出前者的各种系数如何与所谓的kinetic state方程的参数化相关，从而得出不同系数之间的关系，并基于对称性理解为什么活性鸟群流体力学描述中的某些系数自然为一阶，而另一些则自然较小。 当粒子间力以动理论影响核的形式表示时，在流体力学极限下出现粗粒化尺度和相应的导数展开，使我们能够推导出扩散项作为红外相关的算子，提炼出微观相互作用的不同参数化。 最后，我们强调可能的应用。 显示英文摘要

摘要： We derive the hydrodynamic equations of perfect fluids without boost invariance [1] from kinetic theory. Our approach is to follow the standard derivation of the Vlasov hierarchy based on an a-priori unknown collision functional satisfying certain axiomatic properties consistent with the absence of boost invariance. The kinetic theory treatment allows us to identify various transport coefficients in the hydrodynamic regime. We identify a drift term that effects a relaxation to an equilibrium where detailed balance with the environment with respect to momentum transfer is obtained. We then show how the derivative expansion of the hydrodynamics of flocks can be recovered from boost non-invariant kinetic theory and hydrodynamics. We identify how various coefficients of the former relate to a parameterization of the so-called equation of kinetic state that yields relations between different coefficients, arriving at a symmetry-based understanding as to why certain coefficients in hydrodynamic descriptions of active flocks are naturally of order one, and others, naturally small. When inter-particle forces are expressed in terms of a kinetic theory influence kernel, a coarse-graining scale and resulting derivative expansion emerge in the hydrodynamic limit, allowing us to derive diffusion terms as infrared-relevant operators distilling different parameterizations of microscopic interactions. We conclude by highlighting possible applications.