自由能通量和Kubo-Martin-Schwinger关系
Free energy fluxes and the Kubo-Martin-Schwinger relation
摘要：
一般的多分量欧拉流体理论是一组非线性双曲型偏微分方程。然而，如果流体是一个短程多体系统的大尺度描述，这些方程的结构上出现了进一步的限制。在这里，我们得到一个这样的约束，有关的自由能通量。自由能通量产生电流的期望值，类似于产生守恒密度的特定自由能。它们修正了状态方程和欧拉尺度流体力学，并且简单地与熵流相关。使用Kubo-Martin-Schwinger关系与许多守恒量，在量子和经典系统中，我们表明，相关的自由能通量是垂直的向量的逆温度表征的状态。这意味着所有熵流都可以表示为局部可观测量的平均值。在少组分流体中，它意味着电流的平均值仅由比自由能得出，而不使用伽利略或相对论不变性。在可积模型中，这意味着热力学贝特不等式必须满足么正性条件。该关系还保证了空间非均匀宏观外场中欧拉流体力学的物理一致性，因为它意味着熵守恒和局部密度近似的吉布斯形式的稳态。自由能通量的主要结果是基于一般性质，如集群，我们表明，它是严格的数学量子自旋链。
英文摘要：
A general, multi-component Eulerian fluid theory is a set of nonlinear, hyperbolic partial differential equations. However, if the fluid is to be the large-scale description of a short-range many-body system, further constraints arise on the structure of these equations. Here we derive one such constraint, pertaining to the free energy fluxes. The free energy fluxes generate expectation values of currents, akin to the specific free energy generating conserved densities. They fix the equations of state and the Euler-scale hydrodynamics, and are simply related to the entropy currents. Using the Kubo-Martin-Schwinger relations associated to many conserved quantities, in quantum and classical systems, we show that the associated free energy fluxes are perpendicular to the vector of inverse temperatures characterising the state. This implies that all entropy currents can be expressed as averages of local observables. In few-component fluids, it implies that the averages of currents follow from the specific free energy alone, without the use of Galilean or relativistic invariance. In integrable models, in implies that the thermodynamic Bethe ansatz must satisfy a unitarity condition. The relation also guarantees physical consistency of the Euler hydrodynamics in spatially-inhomogeneous, macroscopic external fields, as it implies conservation of entropy, and the local-density approximated Gibbs form of stationarity states. The main result on free energy fluxes is based on general properties such as clustering, and we show that it is mathematically rigorous in quantum spin chains.
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